Distinct learning, retention, and generalization in de novo learning
Raphael Gastrock
Overview
This document discusses detailed results for the tablet and online experiments presented in the manuscript, with both Bayesian and frequentist analyses. We also show additional figures and statistical tests that support our findings.
Set up the R enviornment
Our scripts require the use of certain packages. If some packages are not available in your own system, run the command:
install.packages(c(‘tidyr’, ‘lattice’, ‘circular’, ‘RColorBrewer’, ‘svglite’, ‘scales’, ‘ez’, ‘vioplot’, ‘phia’, ‘emmeans’, ‘afex’, ‘lsr’, ‘BayesFactor’, ‘bayestestR’, ‘tidyverse’, ‘plotrix’, ‘osfr’))
We have written code that pre-processes the data, plots figures, and runs statistical tests. Import the sources below:
source('ana/shared.R')
source('ana/dataOSF.R')
#tablet experiment scripts
source('ana/ordereffects.R')
source('ana/learningRates.R')
source('ana/exponentialandstepModel.R')
source('ana/individualDataCheck.R')
source('ana/rae.R')
source('ana/RTandMT.R')
source('ana/pathlength.R')
#online experiment scripts
source('ana/controlmir.R')
source('ana/controlmirgen.R')
source('ana/su&fa2020online.R')
source('ana/qualtricsdata.R')
source('ana/mironline_fa2020.R')
source('ana/mirgeneralization_fa2020.R')
#manuscript plots
source('ana/manuscriptPlots.R')Then, we ensure that the data is available locally.
# Remove comments below if data is not available locally.
#local <- getwd()
#downloadOSFdata(repository = 'https://osf.io/786nf/', foldername = 'data', folder = local)Study 1: Tablet experiment results
For the tablet experiment, half of the participants (N = 16) were simply told to compensate for the cursor moving differently during perturbed reaches, and the other half (N = 16) were instructed about the nature of each perturbation and was given a strategy to counter for it. We focus on the non-instructed participants for most of the analyses, as we only wanted to observe the effects of instructions on initial learning in each perturbation for the instructed participants.
Order Effects
Given that we implemented a within-subjects design for the tablet experiment, we first test whether learning one perturbation has an effect on learning the other. We also test for any effects in learning, depending on which axis each perturbation was experienced and the target locations relative to the perturbation axis.
Perturbation order
Rotation
For perturbation order, we expect that learning in each perturbation should not affect the other, regardless of which perturbation the participant experienced first.
plotNIROTOrderEffects()
For non-instructed participants, the percentage of compensation did not differ regardless of whether the rotation perturbation was experienced before or after mirror reversed perturbed reaches.
To quantify these comparisons between conditions better, we fit an exponential decay function that allowed us to measure learning rates and learning asymptotes. For perturbation order, we fit the exponential function to participants that either experienced the rotation before or after mirror reversed reaches.
plotROTOrderEffectsModel(group='noninstructed')
We then conducted t-tests to compare the learning rates and asymptotes between the two order conditions. Both frequentist and Bayesian tests are reported below.
getLambdaOrderEffectsTTest(perturbation='ROT')## Frequentist t-test (perturbation: ROT, condition: first vs. second):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -0.61244, df = 9.6387, p-value = 0.5544
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1935460 0.1104204
## sample estimates:
## mean of x mean of y
## 0.1137463 0.1553091
##
## Effect Size - Cohen d:
## [1] 0.3062193
## Bayesian t-test (perturbation: ROT, condition: first vs. second):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4855399 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteOrderEffectsTTest(perturbation='ROT')## Frequentist t-test (perturbation: ROT, condition: first vs. second):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -0.10034, df = 13.759, p-value = 0.9215
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -14.73630 13.42118
## sample estimates:
## mean of x mean of y
## 81.30748 81.96503
##
## Effect Size - Cohen d:
## [1] 0.05016932
## Bayesian t-test (perturbation: ROT, condition: first vs. second):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4290593 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSThe tests confirmed that learning rates and learning asymptote did not differ regardless of whether the rotation was experienced before or after the other perturbation.
Mirror reversal
plotNIMIROrderEffects()
For the mirror reversed perturbed reaches, we also do not find differences depending on the order that they experienced the perturbation. However, note that the percentages of compensation have larger variability compared to those in the rotation perturbation.
We fit the same exponential decay function to both conditions and conducted t-tests to compare learning rates and asymptotes between perturbation order conditions.
plotMIROrderEffectsModel(groups='noninstructed')
We did not find any differences in learning rates and asymptotes between the mirror perturbation order conditions.
getLambdaOrderEffectsTTest(perturbation='MIR')## Frequentist t-test (perturbation: MIR, condition: first vs. second):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 1.0222, df = 8.0209, p-value = 0.3365
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1615243 0.4189405
## sample estimates:
## mean of x mean of y
## 0.2549276 0.1262195
##
## Effect Size - Cohen d:
## [1] 0.5110849
## Bayesian t-test (perturbation: MIR, condition: first vs. second):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6055607 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteOrderEffectsTTest(perturbation='MIR')## Frequentist t-test (perturbation: MIR, condition: first vs. second):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -1.436, df = 7.6622, p-value = 0.1905
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -221.17018 52.22542
## sample estimates:
## mean of x mean of y
## 108.1419 192.6143
##
## Effect Size - Cohen d:
## [1] 0.7180026
## Bayesian t-test (perturbation: MIR, condition: first vs. second):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.835469 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSModel comparisons
Since the mirror reversal data had more variability, we wanted to investigate whether different functions will fit the data better. For some participants, compensation seemed to immediately become better after a few trials. That is, it seemed like they figured things out after a certain trial, and suddenly started to perform better. The nature of such a performance resembled a logistic or step function. Therefore, in addition to the exponential decay function, we also fit both step and logistic functions to the rotation and mirror reversed data for each participant.
For the exponential decay function we get two parameters: lambda for the learning rate, and N0 for the asymptote. For the step function, instead of a learning rate, we get a step parameter to indicate where the change occurs. We also get an asymptote parameter. For the logistic function we get three parameters: x0 (the steepest part of the logistic function), k (the inverse of the steepness of the logistic function), and L (the scale of the function, which starts at 0 (at -infinity) and reaches L at infinity).
After fitting each function to each participant’s data, we also calculate mean squared errors (MSE) between each function and the data. The parameters and MSEs for the rotation perturbation are shown below. Each row will correspond to one participant.
read.csv('data/pilot/processed/ROT_noninstructed_MSE_ordereffects.csv')## step asymptote mse_step lambda N0 mse_expl x0
## 1 12 72.98683 785.9078 0.05839083 81.57260 676.9233 12.552785
## 2 4 81.04288 456.9556 0.09788714 88.71477 252.5075 7.983897
## 3 12 60.44318 653.8266 0.09629438 62.55975 612.8795 10.666315
## 4 4 94.78372 361.9691 0.29441731 96.06407 310.4976 1.637205
## 5 4 70.74633 539.9778 0.11071178 76.33250 411.5146 5.026782
## 6 12 62.28616 881.3983 0.04072276 77.20361 671.5597 18.329900
## 7 12 101.79969 1774.4218 0.12128606 102.46256 1784.0515 10.396347
## 8 4 59.19791 483.4178 0.09026025 65.54994 354.8889 8.010550
## 9 4 71.36746 532.5357 0.04565858 89.73700 261.1401 16.116850
## 10 12 82.19301 614.3897 0.12774811 82.17503 652.5935 10.367659
## 11 12 83.50160 1034.1659 0.11175950 85.60478 897.5420 7.340905
## 12 20 85.93379 1221.9673 0.06040709 89.14594 1259.6360 17.073033
## 13 28 88.40681 2441.6112 0.04275045 92.69678 2558.5557 25.984972
## 14 4 56.09660 753.4171 0.57317597 56.14206 722.7989 -14.448589
## 15 4 69.99917 1784.2213 0.18681641 72.06938 1774.2605 7.971561
## 16 4 80.81635 534.7195 0.09415692 88.14930 429.3196 5.970294
## k L mse_log order
## 1 0.10750730 79.21128 693.2220 1
## 2 0.16637575 87.97088 242.8113 1
## 3 0.25203216 62.23388 596.3819 1
## 4 0.29018463 96.37510 274.6943 1
## 5 0.09724501 77.86428 385.5587 1
## 6 0.06693870 75.75177 653.3326 1
## 7 58.86733376 101.89029 1642.3959 1
## 8 0.10697776 66.13637 343.7633 1
## 9 0.05376664 92.27454 215.8416 2
## 10 2.41995703 82.10854 572.3963 2
## 11 0.19361682 85.30689 858.8186 2
## 12 23.39125037 85.70143 1088.3329 2
## 13 57.73534821 87.87973 2378.1958 2
## 14 0.07471177 56.46177 752.7031 2
## 15 50.91074901 71.76103 1791.1425 2
## 16 0.07429702 91.33297 408.3944 2The parameters and MSEs for the mirror reversed perturbation are shown below:
read.csv('data/pilot/processed/MIR_noninstructed_MSE_ordereffects.csv')## step asymptote mse_step lambda N0 mse_expl x0
## 1 12 70.67695 10038.468 0.091272261 70.34986 10366.833 8.436232
## 2 4 86.00006 6958.623 0.173890614 90.30631 6709.731 363.700593
## 3 20 128.66379 2544.834 0.037484952 146.17279 3271.995 19.983907
## 4 4 165.72773 41620.326 1.000000000 175.16840 37827.448 -482.925932
## 5 4 88.93617 7353.541 0.080457988 99.54437 7112.907 10.905100
## 6 4 112.05057 5676.148 0.542177776 111.07084 5808.457 85.348397
## 7 36 81.65678 25858.208 0.046616700 91.00669 24534.590 18.093643
## 8 28 83.09148 3740.271 0.067520522 81.51580 3552.578 10.342763
## 9 20 50.03808 10315.067 0.112159788 46.92726 10408.876 89.999032
## 10 61 118.63991 19716.386 0.002128261 448.24067 22475.523 148.569114
## 11 12 112.69376 7825.842 0.120900205 111.35251 8246.742 8.517529
## 12 4 114.25455 4549.325 0.270522244 115.30359 4649.753 138.273264
## 13 53 76.44304 36001.512 0.001770864 449.69310 36952.772 72.398280
## 14 4 156.77118 12550.621 0.160442388 163.67998 12219.653 7.331134
## 15 12 138.18906 7172.315 0.128816656 140.40366 6708.294 6.757345
## 16 44 81.46870 54914.347 0.213015853 65.31334 54473.582 28.458298
## k L mse_log order
## 1 3.464302e+01 70.09371 9946.410 1
## 2 8.269970e-03 1208.39199 7001.082 1
## 3 4.240640e+01 129.27685 2524.216 1
## 4 -3.123327e-03 1034.87260 40160.705 1
## 5 1.797476e-01 98.06366 7095.079 1
## 6 -3.362002e-02 143.13554 5558.645 1
## 7 1.365371e+01 91.89385 23174.993 1
## 8 6.907865e-02 83.96143 3534.144 1
## 9 9.606431e-01 289.88433 11966.907 2
## 10 1.000000e+01 585.69114 24684.184 2
## 11 3.223467e+01 113.30476 7274.839 2
## 12 8.285432e-04 241.80361 3650.135 2
## 13 6.567408e+01 117.35588 35715.443 2
## 14 4.752093e+01 162.73248 11884.853 2
## 15 1.765904e+01 139.48680 5765.739 2
## 16 -3.209091e+01 121.50796 53998.968 2We then use the MSEs to calculate AIC values and generate relative log-likelihoods for each participant. This produces values that we can compare across the three functions for each participant. The likelihoods are shown below. A value of 1 indicates the function with the best fit.
read.csv('data/pilot/processed/participant_model_likelihoods.csv')## participant loglikelihood_step loglikelihood_expl loglikelihood_log
## 1 p001_ROT_1 0.8613266 1.0000000 0.3592300
## 2 p002_ROT_1 0.5525864 1.0000000 0.3825699
## 3 p003_ROT_1 0.9373731 1.0000000 0.3780560
## 4 p004_ROT_1 0.8578013 1.0000000 0.4158283
## 5 p005_ROT_1 0.7620954 1.0000000 0.3926451
## 6 p006_ROT_1 0.7619253 1.0000000 0.3781427
## 7 p007_ROT_1 1.0000000 0.9946024 0.3974519
## 8 p008_ROT_1 0.7341245 1.0000000 0.3797855
## 9 p001_ROT_2 0.4903711 1.0000000 0.4450860
## 10 p002_ROT_2 1.0000000 0.9414584 0.3948686
## 11 p003_ROT_2 0.8678898 1.0000000 0.3844668
## 12 p004_ROT_2 1.0000000 0.9700955 0.4130507
## 13 p005_ROT_2 1.0000000 0.9542928 0.3776891
## 14 p006_ROT_2 0.9593610 1.0000000 0.3532640
## 15 p007_ROT_2 0.9944173 1.0000000 0.3644121
## 16 p008_ROT_2 0.8028875 1.0000000 0.3867287
## 17 p001_MIR_1 1.0000000 0.9683254 0.3712843
## 18 p002_MIR_1 0.9642325 1.0000000 0.3525701
## 19 p003_MIR_1 1.0000000 0.7777622 0.3708843
## 20 p004_MIR_1 0.9088696 1.0000000 0.3465064
## 21 p005_MIR_1 0.9672765 1.0000000 0.3688038
## 22 p006_MIR_1 1.0000000 0.9772213 0.3756559
## 23 p007_MIR_1 0.9488124 1.0000000 0.3894617
## 24 p008_MIR_1 0.9498184 1.0000000 0.3697983
## 25 p001_MIR_2 1.0000000 0.9909877 0.3170996
## 26 p002_MIR_2 1.0000000 0.8772382 0.2938421
## 27 p003_MIR_2 1.0000000 0.9489616 0.3957429
## 28 p004_MIR_2 1.0000000 0.9784013 0.4585044
## 29 p005_MIR_2 1.0000000 0.9742574 0.3708260
## 30 p006_MIR_2 0.9736294 1.0000000 0.3782427
## 31 p007_MIR_2 0.9353039 1.0000000 0.4280186
## 32 p008_MIR_2 0.9919736 1.0000000 0.3711129We observe that for majority of participants, the exponential function fits their data best. While we have some participants that show that the step function fits their data best, these likelihoods are not significantly far off from likelihoods in the exponential function. Furthermore, when we pool data across participants and just compare likelihoods for each perturbation type, we observe that the exponential function is the best fit for the data.
read.csv('data/pilot/processed/all_model_likelihoods.csv')## group loglikelihood_step loglikelihood_expl loglikelihood_log
## 1 ROT 0.9175872 1 0.3887772
## 2 MIR 0.9940970 1 0.3698836Thus, we use the exponential function to compare learning rates and asymptotes between order effects conditions, and to compare rotation and mirror reversal perturbations.
Perturbation Axis
Next, we tested for any effects depending on which axis each perturbation was experienced. That is, we compared learning rates and asymptotes between half of the participants that experienced the rotation/mirror reversal on the vertical midline axis, with the other half that experienced the rotation/mirror reversal on the horizontal axis.
Rotation
plotNIROTAxisEffects()
getLambdaAxisEffectsTTest(perturbation = 'ROT')## Frequentist t-test (perturbation: ROT, condition: horizontal vs. vertical):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 0.075719, df = 9.3811, p-value = 0.9412
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1493674 0.1597794
## sample estimates:
## mean of x mean of y
## 0.1371307 0.1319247
##
## Effect Size - Cohen d:
## [1] 0.03785965
## Bayesian t-test (perturbation: ROT, condition: horizontal vs. vertical):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4284234 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteAxisEffectsTTest(perturbation = 'ROT')## Frequentist t-test (perturbation: ROT, condition: horizontal vs. vertical):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -0.32597, df = 13.332, p-value = 0.7495
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -16.20265 11.94481
## sample estimates:
## mean of x mean of y
## 80.57179 82.70071
##
## Effect Size - Cohen d:
## [1] 0.1629855
## Bayesian t-test (perturbation: ROT, condition: horizontal vs. vertical):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4433759 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSThere are no axis effects, regardless of whether the perturbation is experienced on the horizontal or vertical axis of the workspace.
Mirror reversal
We also test for axis effects with the mirror reversed perturbation.
plotNIMIRAxisEffects()
getLambdaAxisEffectsTTest(perturbation = 'MIR')## Frequentist t-test (perturbation: MIR, condition: horizontal vs. vertical):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 0.70209, df = 10.758, p-value = 0.4975
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1930714 0.3732157
## sample estimates:
## mean of x mean of y
## 0.2356096 0.1455375
##
## Effect Size - Cohen d:
## [1] 0.3510446
## Bayesian t-test (perturbation: MIR, condition: horizontal vs. vertical):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5050626 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteAxisEffectsTTest(perturbation = 'MIR')## Frequentist t-test (perturbation: MIR, condition: horizontal vs. vertical):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -1.1488, df = 7.6784, p-value = 0.2852
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -209.11326 70.71935
## sample estimates:
## mean of x mean of y
## 115.7796 184.9765
##
## Effect Size - Cohen d:
## [1] 0.5744119
## Bayesian t-test (perturbation: MIR, condition: horizontal vs. vertical):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6616324 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe also do not find axis effects for the mirror reversal perturbation.
Target location relative to axis
There were six targets for each axis. Three of the six targets were on either end of the axis, but could be on its negative (before axis) or positive (after axis) side.
Rotation
plotNIROTTargetEffects()
For the statistical tests, we calculated a sign flip for targets that required a negative amount of compensation, such that we only compared the magnitude of the compensation. These values were then used to generate the exponential function fit parameters.
getLambdaTargetEffectsTTest(perturbation = 'ROT')## Frequentist t-test (perturbation: ROT, condition: after vs. before):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -1.1508, df = 7.9951, p-value = 0.2831
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.22722622 0.07594933
## sample estimates:
## mean of x mean of y
## 0.0967085 0.1723469
##
## Effect Size - Cohen d:
## [1] 0.5753799
## Bayesian t-test (perturbation: ROT, condition: after vs. before):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6625753 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteTargetEffectsTTest(perturbation = 'ROT')## Frequentist t-test (perturbation: ROT, condition: after vs. before):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 0.38122, df = 13.933, p-value = 0.7088
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -11.50821 16.48087
## sample estimates:
## mean of x mean of y
## 82.87942 80.39309
##
## Effect Size - Cohen d:
## [1] 0.1906115
## Bayesian t-test (perturbation: ROT, condition: after vs. before):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4493055 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe do not find any differences between learning rates and asymptotes, suggesting that there are no target location effects.
Mirror
plotNIMIRTargetEffects()
We again calculated a sign flip for targets that required a negative amount of compensation, then used these values to generate the exponential function fit parameters.
getLambdaTargetEffectsTTest(perturbation = 'MIR')## Frequentist t-test (perturbation: MIR, condition: after vs. before):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 1.9561, df = 7.2705, p-value = 0.0898
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.04520438 0.49775895
## sample estimates:
## mean of x mean of y
## 0.30371221 0.07743493
##
## Effect Size - Cohen d:
## [1] 0.9780628
## Bayesian t-test (perturbation: MIR, condition: after vs. before):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.410721 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteTargetEffectsTTest(perturbation = 'MIR')## Frequentist t-test (perturbation: MIR, condition: after vs. before):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 0.189, df = 13.988, p-value = 0.8528
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -123.0843 146.8714
## sample estimates:
## mean of x mean of y
## 156.3249 144.4313
##
## Effect Size - Cohen d:
## [1] 0.09450181
## Bayesian t-test (perturbation: MIR, condition: after vs. before):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.432839 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe do not find any conclusive evidence of differences between learning rates and asymptotes.
Learning Rates
We then compare the progression of learning across trials between the rotation and mirror tasks. For the plots below, the y-axis will be the amount of compensation in percentage. This is because while the rotation magnitude is consistently 30-degrees, angular reach deviations for the mirror will differ depending on the target distance from the mirror axis. The mirror task will require reach deviations of 15, 30, or 45 degrees. Here, 100% would mean perfect compensation, 0% would be no compensation or reaching directly to the target, and negative values are compensations in the wrong direction relative to the target.
plotTabletLearningRAE()
We observe that although participants learned to compensate for both perturbation types, learning in the mirror reversed perturbation had a larger variability.
We first compare learning between the two perturbation types for non-instructed participants. We fit the exponential decay function to data for each perturbation type. The function produced two measures, a rate of change and asymptote of learning. We then conducted a t-test to compare both measures between the two perturbation types.
getLambdaLearningCurvesTTest()## Frequentist t-test (Rotation vs. Mirror):
##
## Paired t-test
##
## data: subdat1 and subdat2
## t = -0.90541, df = 15, p-value = 0.3796
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.18798463 0.07589294
## sample estimates:
## mean difference
## -0.05604585
##
## Effect Size - Cohen d:
## [1] 0.2263529
## Bayesian t-test (Rotation vs. Mirror):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3646324 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSgetAsymptoteLearningCurvesTTest()## Frequentist t-test (Rotation vs. Mirror):
##
## Paired t-test
##
## data: subdat1 and subdat2
## t = -2.2659, df = 15, p-value = 0.03869
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -133.405929 -4.077705
## sample estimates:
## mean difference
## -68.74182
##
## Effect Size - Cohen d:
## [1] 0.5664646
## Bayesian t-test (Rotation vs. Mirror):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.835884 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWe do not find an effect for the rate of change or asymptote of learning, suggesting no difference in the progression and extent of learning between the two perturbation types.
Supplementary: Learning across three mirror target locations
Given the variability in learning for the mirror reversed perturbation, we investigated whether learning was dependent on the three different target locations.
First, we looked into the overall distribution of percentages of compensation per target location.
getTargetCurveVioplots(group='noninstructed', maxppid=15, location='maxvel')
The distributions are overall as expected, i.e. there were no bimodal distributions. We then plot angular reach deviations per target location.
plotNIMIRTargetCurve()
Although participants learned to compensate for all three target locations, it seems that variability for the target near the mirror axis (15 degrees) is larger. Therefore, we conducted the same analyses as in the previous section but removed all targets where participants had to deviate by 15 degrees.
plotPTypeLearningCurvesWONear()
Removing the 15 degree targets produced less variability, but learning in the mirror reversal still had a larger variability than the rotation.
getLambdaLearningCurvesWONearTTest()## Frequentist t-test (Rotation vs. Mirror):
##
## Paired t-test
##
## data: subdat1 and subdat2
## t = -1.2709, df = 15, p-value = 0.2231
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.24412374 0.06174423
## sample estimates:
## mean difference
## -0.09118975
##
## Effect Size - Cohen d:
## [1] 0.3177292
## Bayesian t-test (Rotation vs. Mirror):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5064033 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSgetAsymptoteLearningCurvesWONearTTest()## Frequentist t-test (Rotation vs. Mirror):
##
## Paired t-test
##
## data: subdat1 and subdat2
## t = -1.6687, df = 15, p-value = 0.1159
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -165.04748 20.09908
## sample estimates:
## mean difference
## -72.4742
##
## Effect Size - Cohen d:
## [1] 0.4171698
## Bayesian t-test (Rotation vs. Mirror):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7986462 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWe conducted the same t-tests to compare learning rates and asymptotes between the two perturbation types. We found that after removing the 15 degree target, there are still no effects in rate and asymptote.
Supplementary: Variability across trials per participant
To gain some insight into how variable reaching movements are across trials for each participant, we can plot individual learning curves during mirror reversed training.
Participant Variability
Reach aftereffects
We then use washout trials following perturbation training to investigate whether reach aftereffects are observed. We expected to observe reach aftereffects following rotation training, but not mirror reversal training.
plotTabletLearningRAE()
As shown in figure panels b and d, we observed our expected results. This is supported by looking into the individual targets for the mirror reversal. Angular reach deviations show that the rate of de-adaptation is around zero across washout trials.
plotNIRAETargetCurve()
It is possible to fit an exponential decay function to the washout data, where it starts at the asymptote and approaches zero over time. The exponential function can be fit into washout trials following rotation training. However, given that the washout trials after mirror reversal training are around zero, it would not make sense to fit the function to this data.
plotROTRAEModel(groups='noninstructed')
plotMIRRAEModel(groups='noninstructed')
We therefore confirmed the presence of reach aftereffects by comparing the percentages of compensation during the last block of aligned reaches with the first block of each of the corresponding washout trials after rotated and mirror reversed training.
RAEt.test(group='noninstructed')## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -8.5651, df = 15, p-value = 3.679e-07
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -57.85656 -34.79894
## sample estimates:
## mean difference
## -46.32775
##
## Effect Size - Cohen d:
## [1] 2.141272
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 43749.26 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -2.0185, df = 15, p-value = 0.06178
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -28.1993350 0.7673049
## sample estimates:
## mean difference
## -13.71602
##
## Effect Size - Cohen d:
## [1] 0.5046321
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.277207 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWe find an effect between aligned and rotated washout blocks, but not between aligned and mirror reversed washout blocks, confirming our expectations that aftereffects are only observed following rotation training. We then compared the corresponding washout trials of rotation and mirror reversed training during the first, second, and last blocks of trials (trials 1-6, 7-12, 43-48).
reachaftereffectsANOVA(group='noninstructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 10.03195 6.376323e-03 * 0.1782152
## 3 block 2 30 18.24462 6.539565e-06 * 0.1396883
## 4 perturbtype:block 2 30 16.11864 1.762222e-05 * 0.1481931
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.6020397 0.028666577 *
## 4 perturbtype:block 0.4964129 0.007428502 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.7153279 9.00959e-05 * 0.7697679 5.444034e-05
## 4 perturbtype:block 0.6650762 2.82235e-04 * 0.7052909 2.018786e-04
## p[HF]<.05
## 3 *
## 4 *reachaftereffectsBayesANOVA(group='noninstructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 507.231 ±2.1%
## [2] block + participant : 16.13844 ±0.61%
## [3] perturbtype + block + participant : 25916.36 ±1.9%
## [4] perturbtype + block + perturbtype:block + participant : 7631097 ±1.21%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 1.00 2.98e+05
## block 0.60 1.00 1.00e+04
## block:perturbtype 0.20 1.00 1.15e+03
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant perturbation type by block interaction.
RAEComparisonsAllBlocksEffSize(group='noninstructed')## contrast estimate SE df t.ratio p.value
## Block1: MIR vs. Block2: MIR 5.326 5.06 15 1.053 1.0000
## Block1: MIR vs. Block3: MIR -0.203 6.87 15 -0.030 1.0000
## Block1: ROT vs. MIR -32.612 8.28 15 -3.938 0.0066
## Block2: ROT vs. MIR -22.099 5.30 15 -4.170 0.0041
## Block3: ROT vs. MIR 3.665 5.76 15 0.637 1.0000
##
## P value adjustment: bonferroni method for 5 tests
## contrast etasquared
## 1 Block1: MIR vs. Block2: MIR 6.884968e-02
## 2 Block1: MIR vs. Block3: MIR 5.823273e-05
## 3 Block1: ROT vs. MIR 5.083788e-01
## 4 Block2: ROT vs. MIR 5.368444e-01
## 5 Block3: ROT vs. MIR 2.630462e-02reachaftereffectsBayesfollowup(group='noninstructed')## Bayesian t-test Mirror block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4116655 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mirror block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2554952 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 30.25465 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 45.31945 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3052648 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow up tests confirm that the first and second rotation washout blocks are different from the first and second mirror washout blocks.
Supplementary: Training rate of learning and its association with aftereffects
We also tested whether learning rates during training correlate to the aftereffects, or lack thereof, during washout trials. To do this, we conducted correlation tests that compared the rate of change during learning with the compensation percentages during the first block of washout trials.
getLambdaRAECorrelations(group='noninstructed')##
## Pearson's product-moment correlation
##
## data: MIRfirst$lambda and MIRfirst$compensation
## t = -0.04915, df = 14, p-value = 0.9615
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5055484 0.4857333
## sample estimates:
## cor
## -0.01313462
##
##
## Pearson's product-moment correlation
##
## data: ROTfirst$lambda and ROTfirst$compensation
## t = -0.40671, df = 14, p-value = 0.6904
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5730698 0.4095834
## sample estimates:
## cor
## -0.108062
##
## Bayes factor analysis
## --------------
## [1] Alt., r=0.333 : 0.5194012 ±0%
##
## Against denominator:
## Null, rho = 0
## ---
## Bayes factor type: BFcorrelation, Jeffreys-beta*
##
## Bayes factor analysis
## --------------
## [1] Alt., r=0.333 : 0.5510508 ±0%
##
## Against denominator:
## Null, rho = 0
## ---
## Bayes factor type: BFcorrelation, Jeffreys-beta*We do not find significant relationships between learning rates and corresponding aftereffects.
Movement analyses
We compared other behavioral measures associated with learning in both perturbation types.
plotTabletMovementMeasures()
Reaction time
We defined reaction time (RT) as the time elapsed between the go signal onset and when the hand-cursor has moved 0.5 cm away from the start position.
To quantify changes in RT across rotation and mirror reversed training, we conducted t-tests to compare RTs in the last block of aligned reaches with the RTs in the first and last blocks of rotation or mirror reversed reaches. We also conducted t-tests to compare RTs in the last block of aligned reaches with the RTs in the first blocks of washout reaches following each perturbation training.
RTt.test(group='noninstructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -3.1381, df = 15, p-value = 0.00677
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -60.26283 -11.51174
## sample estimates:
## mean difference
## -35.88729
##
## Effect Size - Cohen d:
## [1] 0.7845152
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 7.557047 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -7.6317, df = 15, p-value = 1.531e-06
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -392.4082 -221.0708
## sample estimates:
## mean difference
## -306.7395
##
## Effect Size - Cohen d:
## [1] 1.907931
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 11995.74 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTWASHdat$compensation
## t = 1.2824, df = 15, p-value = 0.2192
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -10.53517 42.35997
## sample estimates:
## mean difference
## 15.9124
##
## Effect Size - Cohen d:
## [1] 0.3206011
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5124201 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRWASHdat$compensation
## t = -0.88032, df = 15, p-value = 0.3926
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -41.23091 17.12780
## sample estimates:
## mean difference
## -12.05156
##
## Effect Size - Cohen d:
## [1] 0.220081
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3577765 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 0.073926, df = 15, p-value = 0.942
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -33.94379 36.38297
## sample estimates:
## mean difference
## 1.21959
##
## Effect Size - Cohen d:
## [1] 0.01848154
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2560189 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = -2.5865, df = 15, p-value = 0.02065
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -77.877302 -7.511019
## sample estimates:
## mean difference
## -42.69416
##
## Effect Size - Cohen d:
## [1] 0.6466197
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.027041 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSAs expected, participants were slower in initiating movements in the first block of perturbation training, regardless of the perturbation type. However, we do see in the plot that participants were much slower to initiate movements in mirror reversed reaches compared to rotated reaches. RTs taper off and go back to baseline levels for rotated reaches, but is still slower than baseline levels for mirror reversed reaches at the end of training. There are no effects between aligned and washout reaches.
We also compared RTs between rotation and mirror reversed reaches across training trials.
reactiontimeANOVA(group='noninstructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 46.37509 5.892717e-06 * 0.3841103
## 3 block 2 30 22.38240 1.125541e-06 * 0.2526722
## 4 perturbtype:block 2 30 11.51226 1.948353e-04 * 0.1608922
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8561149 0.3370733
## 4 perturbtype:block 0.9233985 0.5724323
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8742137 4.417721e-06 * 0.9800662 1.397428e-06
## 4 perturbtype:block 0.9288488 2.984089e-04 * 1.0547300 1.948353e-04
## p[HF]<.05
## 3 *
## 4 *RTBayesANOVA(group='noninstructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 3651843 ±1.3%
## [2] block + participant : 159.8289 ±1.56%
## [3] perturbtype + block + participant : 38144873180 ±1.32%
## [4] perturbtype + block + perturbtype:block + participant : 1.286179e+13 ±2.07%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 1.00 5.35e+10
## block 0.60 1.00 2.35e+06
## block:perturbtype 0.20 1.00 1.35e+03
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant perturbation type by block interaction.
RTComparisonsAllBlocksEffSize(group='noninstructed')## contrast estimate SE df t.ratio p.value
## Block1: ROT vs. MIR 270.9 38.7 15 7.000 <.0001
## Block2: ROT vs. MIR 196.2 48.4 15 4.053 0.0031
## Block3: ROT vs. MIR 43.9 19.0 15 2.311 0.1064
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Block1: ROT vs. MIR 0.7656395
## 2 Block2: ROT vs. MIR 0.5227581
## 3 Block3: ROT vs. MIR 0.2625601RTBayesfollowup(group='noninstructed')## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 4744.35 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 36.99169 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.966102 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow up tests show that rotation and mirror reversed RTs differed during the first and second blocks of training. Overall, this shows that movement initiation is slower during mirror reversed perturbed reaches, compared to rotation perturbation reaches.
Movement time
We defined movement time (MT) as the time elapsed between the first sample when the hand-cursor is >0.5 cm away from the start position and the first sample when the hand-cursor is greater than the start-to-target distance
To quantify changes in MT across rotation and mirror reversed training, we conducted the same t-tests as in the reaction time analysis. We compared MTs in the last block of aligned reaches with the MTs in the first and last blocks of rotation or mirror reversed reaches. We also conducted t-tests to compare MTs in the last block of aligned reaches with the MTs in the first blocks of washout reaches following each perturbation training.
MTt.test(group='noninstructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = 3.5038, df = 15, p-value = 0.003198
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 13.36498 54.87910
## sample estimates:
## mean difference
## 34.12204
##
## Effect Size - Cohen d:
## [1] 0.8759598
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 14.18104 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -0.18063, df = 15, p-value = 0.8591
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -56.97808 48.07529
## sample estimates:
## mean difference
## -4.451395
##
## Effect Size - Cohen d:
## [1] 0.04515764
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2591356 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTWASHdat$compensation
## t = 2.6516, df = 15, p-value = 0.01813
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 5.243939 48.221812
## sample estimates:
## mean difference
## 26.73288
##
## Effect Size - Cohen d:
## [1] 0.6628966
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.361832 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRWASHdat$compensation
## t = 1.9364, df = 15, p-value = 0.07189
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -1.80499 37.64532
## sample estimates:
## mean difference
## 17.92017
##
## Effect Size - Cohen d:
## [1] 0.4841017
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.138236 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 2.6135, df = 15, p-value = 0.01957
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 4.473732 44.038268
## sample estimates:
## mean difference
## 24.256
##
## Effect Size - Cohen d:
## [1] 0.6533685
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.161219 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = 2.4529, df = 15, p-value = 0.02689
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 3.46726 49.45266
## sample estimates:
## mean difference
## 26.45996
##
## Effect Size - Cohen d:
## [1] 0.6132171
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.448903 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSParticipants were faster in executing movements during rotated reaches, compared to aligned baseline reaches. Interestingly, faster MTs were also observed in the first block of washout trials following rotation training. In contrast, MTs do not differ between aligned reaches and the first block of mirror reversed reaches or its corresponding washout trials. However, we do find faster MTs during the last block of mirror reversed reaches, when compared to aligned reaches. Despite these detailed findings, MTs are generally not much different across trial types.
We also compared MTs between rotation and mirror reversed reaches across training trials.
movementtimePerturbANOVA(group='noninstructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 14 0.86020670 0.3693952 7.423837e-03
## 3 block 2 28 0.01775302 0.9824147 8.965923e-05
## 4 perturbtype:block 2 28 1.50180740 0.2401263 9.475055e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.6538806 0.0632033
## 4 perturbtype:block 0.9900824 0.9372679
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.7428761 0.9569098 0.8105275 0.9660618
## 4 perturbtype:block 0.9901798 0.2403111 1.1525051 0.2401263MTBayesANOVA(group='noninstructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 0.4900233 ±0.86%
## [2] block + participant : 0.1020026 ±3.11%
## [3] perturbtype + block + participant : 0.04914318 ±1.74%
## [4] perturbtype + block + perturbtype:block + participant : 0.01997596 ±4.88%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 0.34 0.338
## block 0.60 0.10 0.077
## block:perturbtype 0.20 0.01 0.049
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any main or interaction effects for perturbation type and block. This supports the observation that MTs did not show much of a difference overall.
Path length
We defined path length (PL) as the total distance, given x and y coordinates of all recorded points on the reach trajectory, traveled between movement onset and offset. Movement onset and offset are the start and end movement times defined in the previous section. The shortest path length to the target is a straight line spanning the start-to-target distance. However, movements are not perfectly straight and may travel in different directions, depending on the perturbation.
Similar to the other measures above, we conducted t-tests to compare PLs between the last block of aligned trials with the first and last blocks of rotation and mirror reversed training. We then compared PLs between the two perturbation types.
PLt.test(group='noninstructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = 1.8039, df = 15, p-value = 0.09136
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.02151242 0.25849772
## sample estimates:
## mean difference
## 0.1184927
##
## Effect Size - Cohen d:
## [1] 0.4509856
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.9511376 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = 0.45273, df = 15, p-value = 0.6572
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.4456104 0.6859617
## sample estimates:
## mean difference
## 0.1201756
##
## Effect Size - Cohen d:
## [1] 0.1131825
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.279673 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 1.0801, df = 15, p-value = 0.2971
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.08026114 0.24517995
## sample estimates:
## mean difference
## 0.0824594
##
## Effect Size - Cohen d:
## [1] 0.2700305
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4216129 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = 1.5556, df = 15, p-value = 0.1407
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.05870654 0.37585698
## sample estimates:
## mean difference
## 0.1585752
##
## Effect Size - Cohen d:
## [1] 0.3888903
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6951082 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSpathlengthPerturbANOVA(group='noninstructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 0.1108586 0.7437769 0.001741464
## 3 block 2 30 0.7518656 0.4801633 0.009738404
## 4 perturbtype:block 2 30 0.7422843 0.4845656 0.013294868
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.5018114 0.008012787 *
## 4 perturbtype:block 0.6308852 0.039778851 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.6674727 0.4333219 0.7083443 0.4402371
## 4 perturbtype:block 0.7303989 0.4474950 0.7892919 0.4566603PLBayesANOVA(group='noninstructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 0.233162 ±1.59%
## [2] block + participant : 0.1486753 ±1.42%
## [3] perturbtype + block + participant : 0.03521156 ±3.32%
## [4] perturbtype + block + perturbtype:block + participant : 0.008882996 ±1.62%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 0.19 0.161
## block 0.60 0.14 0.104
## block:perturbtype 0.20 6.23e-03 0.025
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects across all comparisons, suggesting that the path of reach trajectories did not differ regardless of trial type or perturbation type.
Instructed participants
For the instructed participants, we told them about the nature of each perturbation. We let them know that the rotation will be 30-degree rotation (CW or CCW depending on their ID), and that the mirror reversal will be dependent on which axis the mirror is placed. We also showed them animations of how to compensate for each perturbation type, and tested their understanding of the strategy by having them draw on a clock-face the location that they should move to bring a cursor to the target. For example, if the target is at 2 o’clock, then they had to draw an arrow to 1 o’clock to correct for a 30 degree CW rotation. In contrast, for a mirror placed along the vertical midline, a target at 2 o’clock would mean that they had to draw an arrow to the 10 position. We know from previous work that such instructions provide an advantage in early learning for rotation perturbations, and we wanted to test whether the same advantage will be observed for the mirror reversal.
plotCollapsedBlockedIndLC(group='instructed', maxppid=31)
We find that instructions did provide an advantage during the first few trials of training for both perturbation types, and that participants were immediately performing around perfect compensation. However, we do find that mirror reversed reaches still showed more variability.
Reach aftereffects
We then investigated the corresponding washout trials for the instructed participants.
plotCollapsedBlockedIndRAE(group='instructed', maxppid=31)
We repeated the reach aftereffects analyses we conducted for non-instructed participants with the instructed participants.
RAEt.test(group='instructed')## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -6.9487, df = 15, p-value = 4.664e-06
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -60.37988 -32.03296
## sample estimates:
## mean difference
## -46.20642
##
## Effect Size - Cohen d:
## [1] 1.737167
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 4389.533 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -2.2901, df = 15, p-value = 0.03692
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -29.074359 -1.043404
## sample estimates:
## mean difference
## -15.05888
##
## Effect Size - Cohen d:
## [1] 0.5725322
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.904656 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSThe first block of washout trials following rotation training differed from the last block of aligned baseline reaches, suggesting the presence of aftereffects. We do not find conclusive evidence for aftereffects following mirror perturbation training.
We compare rotation and mirror reversed washout trials further.
reachaftereffectsANOVA(group='instructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 17.552155 7.894270e-04 * 0.25469337
## 3 block 2 30 15.471313 2.415469e-05 * 0.12293176
## 4 perturbtype:block 2 30 3.523014 4.223711e-02 * 0.05530366
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9355022 0.62706686
## 4 perturbtype:block 0.6096292 0.03129395 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9394102 3.908057e-05 * 1.069306 2.415469e-05
## 4 perturbtype:block 0.7192326 6.065359e-02 0.774818 5.646370e-02
## p[HF]<.05
## 3 *
## 4reachaftereffectsBayesANOVA(group='instructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 74413.58 ±1.16%
## [2] block + participant : 6.644744 ±1.15%
## [3] perturbtype + block + participant : 2585345 ±1.66%
## [4] perturbtype + block + perturbtype:block + participant : 4323871 ±2.19%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 1.00 6.09e+05
## block 0.60 0.99 61.90
## block:perturbtype 0.20 0.62 6.50
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant perturbation type by block interaction.
RAEComparisonsAllBlocksEffSize(group='instructed')## contrast estimate SE df t.ratio p.value
## Block1: MIR vs. Block2: MIR 5.45 4.73 15 1.153 1.0000
## Block1: MIR vs. Block3: MIR 6.88 5.05 15 1.364 0.9632
## Block1: ROT vs. MIR -31.15 8.24 15 -3.782 0.0090
## Block2: ROT vs. MIR -27.09 7.59 15 -3.568 0.0140
## Block3: ROT vs. MIR -9.58 6.04 15 -1.588 0.6659
##
## P value adjustment: bonferroni method for 5 tests
## contrast etasquared
## 1 Block1: MIR vs. Block2: MIR 0.08137381
## 2 Block1: MIR vs. Block3: MIR 0.11036641
## 3 Block1: ROT vs. MIR 0.48810223
## 4 Block2: ROT vs. MIR 0.45907447
## 5 Block3: ROT vs. MIR 0.14388642reachaftereffectsBayesfollowup(group='instructed')## Bayesian t-test Mirror block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4507301 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mirror block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5587037 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 23.01477 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 15.8514 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7226369 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow up tests show that compensation in rotation washout trials were larger in the first and second blocks, compared to mirror reversed washout trials. Overall, it is clear that aftereffects observed following rotation training are larger than those observed following mirror training.
Movement analyses
We also compared RTs, MTs, and PLs in both perturbation types for the instructed participants.
Reaction time
plotIBlockedRT()
We conducted t-tests to compare RTs in the last block of aligned reaches with the RTs in the first and last blocks of rotation or mirror reversed reaches. We also conducted t-tests to compare RTs in the last block of aligned reaches with the RTs in the first blocks of washout reaches following each perturbation training.
RTt.test(group='instructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -3.3466, df = 15, p-value = 0.004416
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -192.04541 -42.59921
## sample estimates:
## mean difference
## -117.3223
##
## Effect Size - Cohen d:
## [1] 0.8366442
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 10.80341 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -5.8431, df = 15, p-value = 3.235e-05
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -358.8209 -167.0079
## sample estimates:
## mean difference
## -262.9144
##
## Effect Size - Cohen d:
## [1] 1.460769
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 775.2025 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTWASHdat$compensation
## t = 0.016671, df = 15, p-value = 0.9869
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -22.26369 22.61470
## sample estimates:
## mean difference
## 0.1755051
##
## Effect Size - Cohen d:
## [1] 0.004167709
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2554273 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRWASHdat$compensation
## t = 1.897, df = 15, p-value = 0.07725
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -3.188351 54.784986
## sample estimates:
## mean difference
## 25.79832
##
## Effect Size - Cohen d:
## [1] 0.4742509
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.078136 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = -1.2063, df = 15, p-value = 0.2464
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -62.53725 17.33285
## sample estimates:
## mean difference
## -22.6022
##
## Effect Size - Cohen d:
## [1] 0.3015863
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4746393 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = -3.8588, df = 15, p-value = 0.001546
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -126.53830 -36.48861
## sample estimates:
## mean difference
## -81.51345
##
## Effect Size - Cohen d:
## [1] 0.9646997
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 26.32368 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSThe results are similar to those with the noninstructed participants.
We also compared RTs between rotation and mirror reversed reaches across training trials.
reactiontimeANOVA(group='instructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 22.242789 0.000275758 * 0.1336356
## 3 block 2 30 7.985512 0.001657892 * 0.1071339
## 4 perturbtype:block 2 30 1.619007 0.214927836 0.0245030
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.6264875 0.03787797 *
## 4 perturbtype:block 0.8348009 0.28254017
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.7280603 0.005002071 * 0.7862567 0.003944299
## 4 perturbtype:block 0.8582224 0.218883460 0.9584451 0.216156091
## p[HF]<.05
## 3 *
## 4RTBayesANOVA(group='instructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 317.0234 ±4.06%
## [2] block + participant : 14.37337 ±0.64%
## [3] perturbtype + block + participant : 13317.39 ±1.36%
## [4] perturbtype + block + perturbtype:block + participant : 7037.983 ±2.95%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 1.00 896.46
## block 0.60 0.98 42.70
## block:perturbtype 0.20 0.34 2.06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find main effects for perturbation type and block.
RTComparisonsAllBlocksEffSize(group='instructed')## contrast estimate SE df t.ratio p.value
## Block1: ROT vs. MIR 145.6 47.8 15 3.045 0.0246
## Block2: ROT vs. MIR 183.7 68.1 15 2.697 0.0496
## Block3: ROT vs. MIR 58.9 19.6 15 2.999 0.0270
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Block1: ROT vs. MIR 0.3819464
## 2 Block2: ROT vs. MIR 0.3266135
## 3 Block3: ROT vs. MIR 0.3748060RTBayesfollowup(group='instructed')## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 6.449157 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.620938 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5.968917 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow up tests show that rotation and mirror reversed RTs differed across the first and second blocks of training. Overall, this confirms that movement initiation is slower during mirror reversed perturbed reaches, compared to rotation perturbation reaches.
Movement time
plotIBlockedMT()
We conducted the same t-tests as in the reaction time analysis.
MTt.test(group='instructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -0.026051, df = 15, p-value = 0.9796
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -23.84831 23.27238
## sample estimates:
## mean difference
## -0.287964
##
## Effect Size - Cohen d:
## [1] 0.006512858
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.255473 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -1.7657, df = 15, p-value = 0.09779
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -75.671969 7.102291
## sample estimates:
## mean difference
## -34.28484
##
## Effect Size - Cohen d:
## [1] 0.4414199
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.904434 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTWASHdat$compensation
## t = 0.7855, df = 15, p-value = 0.4444
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -14.02251 30.38971
## sample estimates:
## mean difference
## 8.183598
##
## Effect Size - Cohen d:
## [1] 0.1963753
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3344723 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRWASHdat$compensation
## t = 1.1782, df = 15, p-value = 0.2571
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -9.692121 33.651818
## sample estimates:
## mean difference
## 11.97985
##
## Effect Size - Cohen d:
## [1] 0.2945561
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.461838 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 1.0866, df = 15, p-value = 0.2944
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -12.99002 40.00618
## sample estimates:
## mean difference
## 13.50808
##
## Effect Size - Cohen d:
## [1] 0.2716401
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4240544 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = 0.82174, df = 15, p-value = 0.4241
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -16.61373 37.46155
## sample estimates:
## mean difference
## 10.42391
##
## Effect Size - Cohen d:
## [1] 0.2054362
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3429112 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSContrary to our findings with noninstructed participants, we found no effects for movement times across the different trial types for instructed participants.
We also compared MTs between rotation and mirror reversed reaches across training trials.
movementtimePerturbANOVA(group='instructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 14 2.903503 0.110470854 0.011733371
## 3 block 2 28 8.888595 0.001025946 * 0.036601364
## 4 perturbtype:block 2 28 2.440166 0.105464379 0.007507154
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.4914825 0.009881032 *
## 4 perturbtype:block 0.7713684 0.185012880
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6629025 0.004702904 * 0.7056493 0.003871487
## 4 perturbtype:block 0.8139136 0.118010748 0.9059609 0.111665143
## p[HF]<.05
## 3 *
## 4MTBayesANOVA(group='instructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 1.340512 ±0.79%
## [2] block + participant : 32.66126 ±0.57%
## [3] perturbtype + block + participant : 61.73181 ±1.1%
## [4] perturbtype + block + perturbtype:block + participant : 32.46491 ±2.11%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 0.74 1.89
## block 0.60 0.98 36.13
## block:perturbtype 0.20 0.25 1.34
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of block.
MTPerturbComparisonsAllBlocksEffSize(group='instructed')## contrast estimate SE df t.ratio p.value
## Block1: MIR vs. Block2: MIR 16.70 10.84 14 1.541 1.0000
## Block1: MIR vs. Block3: MIR 35.17 12.21 14 2.879 0.0849
## Block1: ROT vs. Block2: ROT 11.29 3.46 14 3.263 0.0397
## Block1: ROT vs. Block3: ROT 13.99 4.73 14 2.960 0.0723
## Block1: ROT vs. MIR 20.12 11.61 14 1.733 0.7350
## Block2: ROT vs. MIR 14.71 7.70 14 1.911 0.5369
## Block3: ROT vs. MIR -1.06 6.01 14 -0.176 1.0000
##
## P value adjustment: bonferroni method for 7 tests
## contrast etasquared
## 1 Block1: MIR vs. Block2: MIR 0.144995137
## 2 Block1: MIR vs. Block3: MIR 0.371955088
## 3 Block1: ROT vs. Block2: ROT 0.431948009
## 4 Block1: ROT vs. Block3: ROT 0.384990870
## 5 Block1: ROT vs. MIR 0.176677482
## 6 Block2: ROT vs. MIR 0.206885078
## 7 Block3: ROT vs. MIR 0.002214905MTBayesfollowup(group='instructed')## Bayesian t-test Mirror block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6949954 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mirror block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 4.756378 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 8.912856 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5.422673 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.8791075 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.109472 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2659924 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow up tests show that the block effect is driven by changes within rotation MTs across blocks of trials. However, this is not supported with Bayesian tests. Thus, there are no differences in MTs between the two perturbation types.
Path length
plotPTypePathLength(group='instructed')
Interestingly, we find that there is less PL variability in mirror reversed reaches for instructed participants compared to those observed with noninstructed participants. This suggests that they used the instructions to move in an optimal manner towards the target. Similar to the other measures above, we conducted t-tests to compare PLs between the last block of aligned trials with the first and last blocks of rotation and mirror reversed training. We then compared PLs between the two perturbation types.
PLt.test(group='instructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = 0.49754, df = 15, p-value = 0.626
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.1035788 0.1666597
## sample estimates:
## mean difference
## 0.03154043
##
## Effect Size - Cohen d:
## [1] 0.1243843
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2849554 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -1.3083, df = 15, p-value = 0.2104
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.25508971 0.06103991
## sample estimates:
## mean difference
## -0.0970249
##
## Effect Size - Cohen d:
## [1] 0.3270868
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5264373 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 1.4415, df = 15, p-value = 0.17
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.05628912 0.29152108
## sample estimates:
## mean difference
## 0.117616
##
## Effect Size - Cohen d:
## [1] 0.360387
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6087126 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = 1.1824, df = 15, p-value = 0.2555
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.07107669 0.24817718
## sample estimates:
## mean difference
## 0.08855025
##
## Effect Size - Cohen d:
## [1] 0.2955961
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4636941 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSpathlengthPerturbANOVA(group='instructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 4.059351 0.062216098 0.06247162
## 3 block 2 30 1.888061 0.168916472 0.04353613
## 4 perturbtype:block 2 30 6.702051 0.003925159 * 0.02868146
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9524859 0.71122989
## 4 perturbtype:block 0.6704794 0.06091134
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9546411 0.171121690 1.0904106 0.168916472
## 4 perturbtype:block 0.7521508 0.008875787 * 0.8176245 0.007147874
## p[HF]<.05
## 3
## 4 *PLBayesANOVA(group='instructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 4.891503 ±0.76%
## [2] block + participant : 0.6362595 ±1.27%
## [3] perturbtype + block + participant : 3.666194 ±2.3%
## [4] perturbtype + block + perturbtype:block + participant : 1.910479 ±1.6%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 0.86 4.27
## block 0.60 0.51 0.703
## block:perturbtype 0.20 0.16 0.750
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant perturbation type by block interaction, but only in the frequentist test.
PLPerturbComparisonsAllBlocksEffSize(group='instructed')## contrast estimate SE df t.ratio p.value
## Block1: MIR vs. Block2: MIR -0.0128 0.0692 15 -0.185 1.0000
## Block1: MIR vs. Block3: MIR 0.1856 0.0790 15 2.350 0.2300
## Block1: ROT vs. Block2: ROT 0.1092 0.0898 15 1.216 1.0000
## Block1: ROT vs. Block3: ROT 0.0861 0.0754 15 1.142 1.0000
## Block1: ROT vs. MIR 0.1286 0.0714 15 1.801 0.6432
## Block2: ROT vs. MIR 0.2505 0.0828 15 3.024 0.0598
## Block3: ROT vs. MIR 0.0291 0.0734 15 0.396 1.0000
##
## P value adjustment: bonferroni method for 7 tests
## contrast etasquared
## 1 Block1: MIR vs. Block2: MIR 0.002278355
## 2 Block1: MIR vs. Block3: MIR 0.269141772
## 3 Block1: ROT vs. Block2: ROT 0.089723709
## 4 Block1: ROT vs. Block3: ROT 0.079968756
## 5 Block1: ROT vs. MIR 0.177749702
## 6 Block2: ROT vs. MIR 0.378812974
## 7 Block3: ROT vs. MIR 0.010335440Following up on the frequentist test does not reveal any effects. Thus, we conclude that path lengths do not differ across trial types and between perturbation types.
Study 2: Online experiment results
The online experiment consisted of two sessions. In the first session, participants (N = 63) trained with the mirror reversal perturbation in a browser-based task, while using their dominant hand to control either their mouse or trackpad. They then returned for a second session (N = 48), where they immediately had to complete the same mirror reversed reaches, so that we may test for retention. We then tested for generalization by having participants complete mirror reversed reaches to different target locations across the workspace, and with their untrained/ non-dominant hand.
Target locations were either 5 degrees, 45 degrees, or 85 degrees away from a mirror axis placed along the vertical midline. We refer to these as near, middle, and far targets respectively. We compare learning across these three target locations using three dependent measures: amount of compensation, completion time, and path length
Session 1
The first session began with 45 trials of aligned reaches with the participants’ dominant hand. Then they switched to using their non-dominant hand to complete 21 trials of aligned reaches. We then instructed them to switch back to using their dominant hand to complete 90 mirror reversed trials. Finally, they completed 21 trials of washout trials using their trained/ dominant hand.
plotOnlineDependentMeasures()
plotBlockedDependentMeasures()
Aligned reaches
Amount of compensation
Before comparing learning across the three target locations, we first tested whether compensation in aligned reaches differed depending on the hand used to control the cursor. Thus we took the aligned reaches from each hand, and compared the first, second, and last block of reaching trials (trials 1-9, 10-18, 37-45 for the dominant hand, trials 46-48, 49-51, 64-66 for the nondominant hand) to the three target locations. We conducted a 3x3x2 (target x block x hand) within-subjects ANOVA.
alignedLearningANOVA2Hands()## Comparing targets and blocks between trained and untrained hands:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 0.2179356 0.8044846 0.0004305633
## 3 block 2 124 1.3531164 0.2622224 0.0024565576
## 4 hand 1 62 1.9838470 0.1639809 0.0026447799
## 5 target:block 4 248 1.2672615 0.2834110 0.0043808665
## 6 target:hand 2 124 1.9789967 0.1425491 0.0039777107
## 7 block:hand 2 124 1.3071810 0.2742839 0.0015969121
## 8 target:block:hand 4 248 0.7323503 0.5706330 0.0023947652
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9897920 0.7312906822
## 3 block 0.9037101 0.0455920517 *
## 5 target:block 0.5974755 0.0002844163 *
## 6 target:hand 0.9901295 0.7389344283
## 7 block:hand 0.9614900 0.3018665755
## 8 target:block:hand 0.7066081 0.0127693436 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 target 0.9898951 0.8022947 1.0223789 0.8044846
## 3 block 0.9121675 0.2618553 0.9383619 0.2620144
## 5 target:block 0.8270634 0.2862176 0.8792547 0.2855044
## 6 target:hand 0.9902260 0.1430381 1.0227374 0.1425491
## 7 block:hand 0.9629180 0.2739438 0.9931696 0.2742274
## 8 target:block:hand 0.8525704 0.5501990 0.9082129 0.5582730alignedLearning2HandsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.01300477 ±0.81%
## [2] block + participant : 0.04029981 ±0.88%
## [3] target + block + participant : 0.0005969879 ±9.75%
## [4] target + block + target:block + participant : 1.13764e-05 ±2.44%
## [5] hand + participant : 0.29328 ±0.88%
## [6] target + hand + participant : 0.003845631 ±1.84%
## [7] block + hand + participant : 0.01174063 ±1.24%
## [8] target + block + hand + participant : 0.0001572003 ±1.88%
## [9] target + block + target:block + hand + participant : 3.79254e-06 ±7.26%
## [10] target + hand + target:hand + participant : 0.0006628979 ±1.53%
## [11] target + block + hand + target:hand + participant : 2.673914e-05 ±2.28%
## [12] target + block + target:block + hand + target:hand + participant : 6.40545e-07 ±4.2%
## [13] block + hand + block:hand + participant : 0.0005626987 ±2.03%
## [14] target + block + hand + block:hand + participant : 7.218582e-06 ±2.21%
## [15] target + block + target:block + hand + block:hand + participant : 1.627456e-07 ±3.49%
## [16] target + block + hand + target:hand + block:hand + participant : 1.266569e-06 ±2.38%
## [17] target + block + target:block + hand + target:hand + block:hand + participant : 2.908531e-08 ±3.39%
## [18] target + block + target:block + hand + target:hand + block:hand + target:block:hand + participant : 6.547288e-10 ±2.96%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.01 0.005
## block 0.74 0.04 0.015
## block:target 0.32 1.17e-05 2.54e-05
## hand 0.74 0.23 0.105
## hand:target 0.32 5.07e-04 0.001
## block:hand 0.32 4.19e-04 9.08e-04
## block:hand:target 0.05 4.80e-10 8.64e-09
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find an effect for the hand used, suggesting that compensation in aligned trials are not different regardless of which hand was used.
Completion time
We repeat the same test for completion time. In the online study, there was no pause in between trials. One trial would end as participants moved close enough to the home position, and the target for the next trial would immediately appear. However, the return movement from that previous trial often overshot the home position, such that it appeared participants responded to the appearance of the target immediately. This made the definitions of reaction time used for the tablet study uninformative, and consequently that of movement time, as well as other ways to define RT and MT. We instead used completion time, defined as the time elapsed between target onset and target acquisition (RT plus MT).
alignedMTANOVA2Hands()## Comparing targets and blocks between trained and untrained hands:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 3.1793455 4.502617e-02 * 1.902889e-03
## 3 block 2 124 10.9050773 4.338131e-05 * 1.738211e-02
## 4 hand 1 62 8.3774637 5.238065e-03 * 6.158510e-03
## 5 target:block 4 248 0.2066594 9.345755e-01 1.018792e-04
## 6 target:hand 2 124 2.7305726 6.910332e-02 8.437125e-04
## 7 block:hand 2 124 0.1433789 8.665692e-01 7.573291e-05
## 8 target:block:hand 4 248 0.3831093 8.206260e-01 1.746956e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.6649390 3.934091e-06 *
## 3 block 0.2833814 1.983024e-17 *
## 5 target:block 0.2383686 8.055260e-15 *
## 6 target:hand 0.7857191 6.392243e-04 *
## 7 block:hand 0.6450537 1.558380e-06 *
## 8 target:block:hand 0.3877660 4.649175e-09 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.7490294 0.0601965745 0.7634276 0.0592095729
## 3 block 0.5825406 0.0008758157 * 0.5868350 0.0008489665
## 5 target:block 0.6141871 0.8554825790 0.6414461 0.8637610904
## 6 target:hand 0.8235327 0.0801469054 0.8430834 0.0788517477
## 7 block:hand 0.7380366 0.8016187696 0.7517078 0.8058280661
## 8 target:block:hand 0.6467472 0.7355183318 0.6773781 0.7448918107
## p[HF]<.05
## 2
## 3 *
## 5
## 6
## 7
## 8alignedMT2HandsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.2238295 ±0.98%
## [2] block + participant : 70441922202 ±0.8%
## [3] target + block + participant : 18835299558 ±1.07%
## [4] target + block + target:block + participant : 51358972 ±1.74%
## [5] hand + participant : 1898.163 ±0.92%
## [6] target + hand + participant : 462.1702 ±2.35%
## [7] block + hand + participant : 2.55903e+14 ±4.07%
## [8] target + block + hand + participant : 7.073388e+13 ±2.63%
## [9] target + block + target:block + hand + participant : 189323928928 ±2.77%
## [10] target + hand + target:hand + participant : 38.3683 ±7.35%
## [11] target + block + hand + target:hand + participant : 6.217508e+12 ±3.77%
## [12] target + block + target:block + hand + target:hand + participant : 16331577197 ±3.18%
## [13] block + hand + block:hand + participant : 5.485588e+12 ±1.67%
## [14] target + block + hand + block:hand + participant : 1.620423e+12 ±2.56%
## [15] target + block + target:block + hand + block:hand + participant : 4428392553 ±5.19%
## [16] target + block + hand + target:hand + block:hand + participant : 140114585727 ±4.08%
## [17] target + block + target:block + hand + target:hand + block:hand + participant : 348180865 ±2.45%
## [18] target + block + target:block + hand + target:hand + block:hand + target:block:hand + participant : 3726054 ±5.16%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.23 0.108
## block 0.74 1.00 5.07e+10
## block:target 0.32 6.18e-04 0.001
## hand 0.74 1.00 1.36e+03
## hand:target 0.32 0.02 0.041
## block:hand 0.32 0.02 0.047
## block:hand:target 0.05 1.09e-08 1.97e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of hand.
MTComparisonsHandEffect()##
## Paired t-test
##
## data: trained$movementtime and untrained$movementtime
## t = -2.8944, df = 62, p-value = 0.002619
## alternative hypothesis: true mean difference is less than 0
## 95 percent confidence interval:
## -Inf -0.08422589
## sample estimates:
## mean difference
## -0.199074
##
## Bayesian t-test (trained hand vs. untrained hand):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 -Inf<d<0 : 321.9046 ±0%
##
## Against denominator:
## Alternative, r = 0.707106781186548, mu =/= 0 !(-Inf<d<0)
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests suggest that completion time in the trained (dominant) hand is faster than in the untrained (nondominant) hand.
Path length
Finally, we compare Path lengths.
alignedPLANOVA2Hands()## Comparing targets and blocks between trained and untrained hands:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 0.9370209 3.945495e-01 0.001410317
## 3 block 2 124 3.7850569 2.537435e-02 * 0.004789706
## 4 hand 1 62 32.4894316 3.555892e-07 * 0.046169631
## 5 target:block 4 248 0.8423108 4.994801e-01 0.002308271
## 6 target:hand 2 124 2.3006869 1.044520e-01 0.002855826
## 7 block:hand 2 124 6.3497149 2.369239e-03 * 0.007964748
## 8 target:block:hand 4 248 0.7438230 5.629464e-01 0.001986878
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9230495 0.086968632
## 3 block 0.9607552 0.294909497
## 5 target:block 0.6420409 0.001533283 *
## 6 target:hand 0.8314675 0.003591538 *
## 7 block:hand 0.9117231 0.059678859
## 8 target:block:hand 0.6499961 0.002031332 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9285478 0.388839776 0.9560315 0.391099567
## 3 block 0.9622372 0.026958635 * 0.9924332 0.025684081
## 5 target:block 0.8107457 0.479678184 0.8607819 0.485342045
## 6 target:hand 0.8557742 0.113058031 0.8776768 0.111725021
## 7 block:hand 0.9188838 0.003167035 * 0.9456045 0.002878002
## 8 target:block:hand 0.8120525 0.537031797 0.8622598 0.544467437
## p[HF]<.05
## 2
## 3 *
## 5
## 6
## 7 *
## 8alignedPL2HandsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.02475946 ±0.68%
## [2] block + participant : 0.2191048 ±2%
## [3] target + block + participant : 0.00548823 ±1.39%
## [4] target + block + target:block + participant : 4.826953e-05 ±3.59%
## [5] hand + participant : 5.409361e+12 ±1.15%
## [6] target + hand + participant : 142864783068 ±1.36%
## [7] block + hand + participant : 1.404726e+12 ±1.44%
## [8] target + block + hand + participant : 37285719386 ±1.82%
## [9] target + block + target:block + hand + participant : 350389319 ±2.42%
## [10] target + hand + target:hand + participant : 17836967336 ±1.54%
## [11] target + block + hand + target:hand + participant : 5139425890 ±5.22%
## [12] target + block + target:block + hand + target:hand + participant : 50163331 ±5.57%
## [13] block + hand + block:hand + participant : 8.269735e+12 ±32.73%
## [14] target + block + hand + block:hand + participant : 146968169818 ±1.78%
## [15] target + block + target:block + hand + block:hand + participant : 1422432924 ±2.33%
## [16] target + block + hand + target:hand + block:hand + participant : 19102947634 ±2.39%
## [17] target + block + target:block + hand + target:hand + block:hand + participant : 203422503 ±3.6%
## [18] target + block + target:block + hand + target:hand + block:hand + target:block:hand + participant : 6483126 ±33%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.02 0.009
## block 0.74 0.64 0.634
## block:target 0.32 1.32e-04 2.85e-04
## hand 0.74 1.00 4.42e+12
## hand:target 0.32 2.74e-03 0.006
## block:hand 0.32 0.55 2.61
## block:hand:target 0.05 4.19e-07 7.55e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of hand.
PLComparisonsHandEffect()##
## Paired t-test
##
## data: trained$pathlength and untrained$pathlength
## t = -5.7, df = 62, p-value = 1.778e-07
## alternative hypothesis: true mean difference is less than 0
## 95 percent confidence interval:
## -Inf -0.03286534
## sample estimates:
## mean difference
## -0.04648238
##
## Bayesian t-test (trained hand vs. untrained hand):## t is large; approximation invoked.
## t is large; approximation invoked.## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 -Inf<d<0 : 5624467 ±NA%
##
## Against denominator:
## Alternative, r = 0.707106781186548, mu =/= 0 !(-Inf<d<0)
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests comparing PLs in the two hands suggest that path lengths were longer for the untrained/ nondominant hand.
Learning
Amount of compensation
We observe really fast learning in the online paradigm, which is due to participants exploring the workspace during the very first trial (see also Analyses_SupplementaryOnlineExperiments.Rmd). Regardless, participants learned to compensate for the mirror reversal in each of the target locations accordingly. Next, given that we observe fast learning, we cannot fit the exponential function to this data and generate reliable measures of learning rate and learning asymptote. Instead, we compare reaching performance to the three target locations across the first, second, and last few blocks of training trials (trials 1-3, 4-6, 76-90). We conduct a 3x3 (target x block) within-subjects ANOVA. We converted the angular reach deviations to percentage of compensation, such that the three target locations will be comparable.
mirrorANOVA()## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 3.0295259 0.0519312 0.008910013
## 3 block 2 124 0.3898554 0.6779818 0.001475398
## 4 target:block 4 248 0.7498522 0.5589303 0.005797917
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.081089137 5.288856e-34 *
## 3 block 0.788174290 7.030384e-04 *
## 4 target:block 0.001314326 1.719368e-80 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 target 0.5211289 0.08499643 0.5221834 0.0849105
## 3 block 0.8252012 0.63813105 0.8448718 0.6430256
## 4 target:block 0.4217775 0.45392147 0.4322788 0.4569101mirrorBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.2319867 ±0.6%
## [2] block + participant : 0.03023574 ±2.62%
## [3] target + block + participant : 0.007079286 ±1.64%
## [4] target + block + target:block + participant : 0.0002117259 ±1.45%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.19 0.155
## block 0.60 0.03 0.020
## block:target 0.20 1.67e-04 6.67e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects, suggesting that reaching performance did not differ across the the three target locations throughout training.
Given the large inter-participant variability observed with the near target, as discussed in the manuscript, we repeat the analyses without the near target, to investigate differences in percentage of compensation between the far and middle targets.
mirrorANOVA(groups=c('far', 'mid'))## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 1 62 0.134772 0.714784774 0.0004399541
## 3 block 2 124 4.786889 0.009940983 * 0.0205071624
## 4 target:block 2 124 4.136051 0.018243691 * 0.0194465815
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9288764 0.10536990
## 4 target:block 0.8732164 0.01600358 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9335991 0.01162907 * 0.9614842 0.01088735 *
## 4 target:block 0.8874818 0.02251037 * 0.9117696 0.02151116 *mirrorBayesANOVA(groups=c('far', 'mid'))## Bayes factor analysis
## --------------
## [1] target + participant : 0.1315981 ±7.82%
## [2] block + participant : 1.541094 ±1.67%
## [3] target + block + participant : 0.1870049 ±3.21%
## [4] target + block + target:block + participant : 0.3809149 ±2.29%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.22 0.184
## block 0.60 0.65 1.24
## block:target 0.20 0.12 0.533
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no target effect, but do find a significant target by block interaction. However, the interaction does not hold up under the Bayesian test. Regardless, follow-up frequentits tests comparing the far and middle target across blocks show only a small difference during the last block, where compensation was slightly higher for the far target.
mirrorNoNearTargetComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far first 48.2 6.39 62 35.5 61.0
## mid first 70.0 10.55 62 48.9 91.1
## far second 84.9 4.68 62 75.6 94.3
## mid second 69.8 12.41 62 45.0 94.6
## far last 85.5 2.63 62 80.2 90.7
## mid last 71.1 5.06 62 61.0 81.3
##
## Confidence level used: 0.95mirrorNoNearTargetComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## first block: far vs. mid 21.7 12.96 62 1.678 0.2951
## second block: far vs. mid -15.1 13.12 62 -1.152 0.7613
## last block: far vs. mid -14.3 4.49 62 -3.185 0.0068
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 first block: far vs. mid 0.04344156
## 2 second block: far vs. mid 0.02095313
## 3 last block: far vs. mid 0.14060265mirrorNoNearTargetBayesfollowup()## Bayesian t-test first block, far vs. mid:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7711953 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test second block, far vs. mid:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3426166 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block, far vs. mid:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.172452 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSCompletion time
Next, we conduct a 3x3 (target x block) within-subjects ANOVA to test for completion time effects during the mirror reversed trials.
mirrorMTANOVA()## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 24.240009 1.301187e-09 * 0.06931910
## 3 block 2 124 41.536873 1.557371e-14 * 0.13156353
## 4 target:block 4 248 3.768315 5.385664e-03 * 0.01756984
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9744759 4.544840e-01
## 3 block 0.6582257 2.886900e-06 *
## 4 target:block 0.2727198 3.320161e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9751112 1.985595e-09 * 1.0063651 1.301187e-09
## 3 block 0.7452818 1.957267e-11 * 0.7594312 1.315793e-11
## 4 target:block 0.5725432 2.047303e-02 * 0.5957181 1.902400e-02
## p[HF]<.05
## 2 *
## 3 *
## 4 *mirrorMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 7680042 ±0.83%
## [2] block + participant : 5.173466e+16 ±1.57%
## [3] target + block + participant : 1.728536e+25 ±1.11%
## [4] target + block + target:block + participant : 2.226138e+25 ±1.25%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 5.10e+08
## block 0.60 1.00 3.43e+18
## block:target 0.20 0.56 5.15
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant block by target interaction.
mirrorMTComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far first 3.97 0.4997 62 2.97 4.97
## mid first 7.74 0.7367 62 6.27 9.22
## near first 5.33 0.8507 62 3.63 7.03
## far second 2.88 0.2227 62 2.44 3.33
## mid second 5.80 0.5250 62 4.75 6.85
## near second 4.24 0.4765 62 3.29 5.19
## far last 1.39 0.0686 62 1.26 1.53
## mid last 2.40 0.1683 62 2.06 2.73
## near last 2.39 0.1791 62 2.03 2.75
##
## Confidence level used: 0.95mirrorMTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 3.77155 0.684 62 5.516 <.0001
## 1st block: Far vs. Near 1.35750 0.858 62 1.581 1.0000
## 1st block: Mid vs. Near -2.41405 1.024 62 -2.357 0.1942
## 2nd block: Far vs. Mid 2.91477 0.497 62 5.866 <.0001
## 2nd block: Far vs. Near 1.35358 0.497 62 2.725 0.0752
## 2nd block: Mid vs. Near -1.56119 0.538 62 -2.903 0.0460
## last block: Far vs. Mid 1.00064 0.149 62 6.709 <.0001
## last block: Far vs. Near 0.99615 0.152 62 6.543 <.0001
## last block: Mid vs. Near -0.00449 0.145 62 -0.031 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 3.291755e-01
## 2 1st block: Far vs. Near 3.876890e-02
## 3 1st block: Mid vs. Near 8.225596e-02
## 4 2nd block: Far vs. Mid 3.569403e-01
## 5 2nd block: Far vs. Near 1.069388e-01
## 6 2nd block: Mid vs. Near 1.196496e-01
## 7 last block: Far vs. Mid 4.206092e-01
## 8 last block: Far vs. Near 4.084704e-01
## 9 last block: Mid vs. Near 1.534659e-05mirrorMTBayesfollowup()## FIRST BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 21239.82 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4480167 ±0.04%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.781386 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## SECOND BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 75680.61 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 4.019194 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 6.166676 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## LAST BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1745008 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 934525.6 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1380859 ±0.09%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show faster completion times for the far target compared to the middle target across all three blocks. The far target is also faster than the near target for the last block. These results suggest that movement initiation and execution towards the far target is faster than the other two targets.
We also compare the first and last block of training CTs to those in the aligned trials. We conduct t-tests comparing each block:
LearningMTTrainedTargetsBayestTest()## Frequentist t-test (Aligned vs. Mirror block 1):
##
## Paired t-test
##
## data: alignedblk and mirrorblk1
## t = -11.772, df = 188, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -5.370041 -3.828620
## sample estimates:
## mean difference
## -4.59933
##
## Effect Size - Cohen d:
## [1] 0.8562982
## Bayesian t-test (Aligned vs. Mirror block 1):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.546987e+21 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Frequentist t-test (Aligned vs. Mirror last block):
##
## Paired t-test
##
## data: alignedblk and mirrorblk2
## t = -10.818, df = 188, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -1.1576483 -0.8005685
## sample estimates:
## mean difference
## -0.9791084
##
## Effect Size - Cohen d:
## [1] 0.7868962
## Bayesian t-test (Aligned vs. Mirror last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.687179e+18 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWe find that CTs do not go back to baseline by the end of training, but are comparable to those in baseline.
Path length
We then conducted a 3x3 (target x block) within-subjects ANOVA for path lengths during the mirror reversed trials.
mirrorPLANOVA()## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 22.848207 3.568117e-09 * 0.06955679
## 3 block 2 124 30.872062 1.316465e-11 * 0.12362195
## 4 target:block 4 248 4.766978 1.010407e-03 * 0.02462987
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9997251 9.916481e-01
## 3 block 0.4613638 5.666666e-11 *
## 4 target:block 0.1788990 2.617593e-18 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9997251 3.583854e-09 * 1.0330353 3.568117e-09
## 3 block 0.6499262 2.422326e-08 * 0.6580767 2.032174e-08
## 4 target:block 0.6458999 5.127498e-03 * 0.6764410 4.450701e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *mirrorPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1618993 ±0.72%
## [2] block + participant : 6.777705e+13 ±0.71%
## [3] target + block + participant : 1.741991e+21 ±1.25%
## [4] target + block + target:block + participant : 8.564969e+21 ±2.02%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.01e+08
## block 0.60 1.00 4.24e+15
## block:target 0.20 0.83 19.67
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target by block interaction.
mirrorPLComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far first 1.316 0.2468 62 0.822 1.809
## mid first 2.274 0.2219 62 1.831 2.718
## near first 1.330 0.1393 62 1.051 1.608
## far second 0.683 0.0429 62 0.597 0.768
## mid second 1.479 0.1332 62 1.213 1.746
## near second 0.881 0.0678 62 0.746 1.017
## far last 0.561 0.0235 62 0.514 0.608
## mid last 0.785 0.0339 62 0.717 0.853
## near last 0.750 0.0449 62 0.660 0.839
##
## Confidence level used: 0.95mirrorPLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 0.9583 0.2424 62 3.953 0.0018
## 1st block: Far vs. Near 0.0138 0.2769 62 0.050 1.0000
## 1st block: Mid vs. Near -0.9444 0.2629 62 -3.592 0.0058
## 2nd block: Far vs. Mid 0.7965 0.1385 62 5.751 <.0001
## 2nd block: Far vs. Near 0.1987 0.0759 62 2.616 0.1003
## 2nd block: Mid vs. Near -0.5978 0.1319 62 -4.532 0.0002
## last block: Far vs. Mid 0.2245 0.0249 62 9.002 <.0001
## last block: Far vs. Near 0.1889 0.0428 62 4.409 0.0004
## last block: Mid vs. Near -0.0356 0.0398 62 -0.895 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 2.013354e-01
## 2 1st block: Far vs. Near 4.009271e-05
## 3 1st block: Mid vs. Near 1.722531e-01
## 4 2nd block: Far vs. Mid 3.478839e-01
## 5 2nd block: Far vs. Near 9.943038e-02
## 6 2nd block: Mid vs. Near 2.487997e-01
## 7 last block: Far vs. Mid 5.665241e-01
## 8 last block: Far vs. Near 2.387150e-01
## 9 last block: Mid vs. Near 1.276537e-02mirrorPLBayesfollowup()## FIRST BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 113.437 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1381876 ±0.09%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 38.89459 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## SECOND BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 49700.79 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.130336 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 711.1672 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## LAST BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 11087320911 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 476.8272 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2023162 ±0.07%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show that the far target had shorter path lengths than the middle target across block of trials. The far target also had a shorter path length than the near target during the end of learning. Finally, the near target had shorter path lengths that the middle target for the first two blocks. Taken together, these results suggest that path lengths were shortest for the far target, and longest for the middle target.
We also compare the first and last block of training PLs to those in the aligned trials. We conduct t-tests comparing each block:
LearningPLTrainedTargetsBayestTest()## Frequentist t-test (Aligned vs. Mirror block 1):
##
## Paired t-test
##
## data: alignedblk and mirrorblk1
## t = -9.495, df = 188, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -1.4170587 -0.9295353
## sample estimates:
## mean difference
## -1.173297
##
## Effect Size - Cohen d:
## [1] 0.6906602
## Bayesian t-test (Aligned vs. Mirror block 1):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5.04267e+14 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Frequentist t-test (Aligned vs. Mirror last block):
##
## Paired t-test
##
## data: alignedblk and mirrorblk2
## t = -11.407, df = 188, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.272056 -0.191831
## sample estimates:
## mean difference
## -0.2319435
##
## Effect Size - Cohen d:
## [1] 0.8297057
## Bayesian t-test (Aligned vs. Mirror last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.338311e+20 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWe find that PLs do not go back to baseline by the end of training, but are comparable to those in baseline.
Reach aftereffects
Amount of compensation
From the plot, we do not observe evidence of reach aftereffects in all targets. To quantify this, we compared the first two blocks of trials during washout (trials 1-3, 4-6) with aligned reaches to the three targets. We conducted a 3x3 (block x target) within-subjects ANOVA.
RAETrainedTargetsANOVA(groups = c('far', 'mid'))## Comparing angular reach deviations during washout trials with aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 1.9711376 0.14363894 0.0079177259
## 3 target 1 62 3.0307291 0.08666193 0.0098884903
## 4 block:target 2 124 0.1026442 0.90252459 0.0005588434
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8426727 0.0054025365 *
## 4 block:target 0.7842575 0.0006039341 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.8640598 0.1503661 0.8865788 0.1492608
## 4 block:target 0.8225426 0.8658137 0.8420223 0.8705205RAETrainedTargetsBayesANOVA(groups = c('far', 'mid'))## Bayes factor analysis
## --------------
## [1] target + participant : 0.7871576 ±0.87%
## [2] block + participant : 0.1290636 ±0.67%
## [3] target + block + participant : 0.1052354 ±1.31%
## [4] target + block + target:block + participant : 0.006420858 ±2.09%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.44 0.531
## block 0.60 0.12 0.090
## block:target 0.20 3.17e-03 0.013
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects when comparing percentages for the far and middle targets.
Completion time
We then compare washout trials with those in aligned to test for completion time effects between aligned and washout trials. We conduct a 3x3 (target x block) within-subjects ANOVA, where block considers the aligned trials, first, and second block of washout trials.
RAEMTTrainedTargetsANOVA()## Comparing movement times during washout trials with aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 9.93029285 9.994277e-05 * 0.0140440457
## 3 target 2 124 9.07320678 2.101446e-04 * 0.0065829384
## 4 block:target 4 248 0.09110735 9.851931e-01 0.0001319642
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.6351112 9.703270e-07 *
## 3 target 0.9718037 4.179711e-01
## 4 block:target 0.3307473 6.467021e-11 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.7326604 0.0005554876 * 0.7459791 0.0005097983
## 3 target 0.9725770 0.0002458168 * 1.0036217 0.0002101446
## 4 block:target 0.6347400 0.9470049475 0.6641091 0.9523221858
## p[HF]<.05
## 2 *
## 3 *
## 4RAEMTTrainedTargetsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 13.65677 ±0.66%
## [2] block + participant : 34321.53 ±0.8%
## [3] target + block + participant : 708024.4 ±1.49%
## [4] target + block + target:block + participant : 5847.369 ±1.63%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.95 13.87
## block 0.60 1.00 3.40e+04
## block:target 0.20 7.82e-03 0.032
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find main effects of block and target, but no interaction. We then conduct follow-up tests on the block effect, regardless of target location.
RAEMTTrainedTargetsComparisonMeans()## block emmean SE df lower.CL upper.CL
## baseline 1.08 0.1106 62 0.860 1.30
## first 1.17 0.0894 62 0.990 1.35
## second 0.94 0.0770 62 0.786 1.09
##
## Confidence level used: 0.95RAEMTTrainedTargetsComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Aligned vs. Washout_b1 0.0876 0.0598 62 1.466 0.4428
## Aligned vs. Washout_b2 -0.1414 0.0586 62 -2.414 0.0562
## Washout_b1 vs. Washout_b2 -0.2291 0.0327 62 -7.012 <.0001
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Aligned vs. Washout_b1 0.0335211
## 2 Aligned vs. Washout_b2 0.0859177
## 3 Washout_b1 vs. Washout_b2 0.4422571RAEMTTrainedTargetsBlockEffectBayesfollowup()## Bayesian t-test aligned vs washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3809322 ±0.05%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test aligned vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.007065 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test washout block 1 vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5496587 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWe find that the main effect of block is driven by a difference between the two blocks during washout, given that completion time is faster as trials progress. Overall, completion time during washout trials do not differ from completion times during aligned reaches.
Path length
Next, we conducted a 3x3 (target x block) within-subjects ANOVA, to test for target effects for path length across the aligned trials, first and second blocks of washout trials.
RAEPLTrainedTargetsANOVA()## Comparing path length during washout trials with aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 9.4553639 0.0001507041 * 0.031685134
## 3 target 2 124 0.6134957 0.5430899821 0.001977601
## 4 block:target 4 248 0.7343285 0.5693035410 0.003295324
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.5648765 2.720076e-08 *
## 3 target 0.9041194 4.622601e-02 *
## 4 block:target 0.3040437 6.547509e-12 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.6968041 0.0009424686 * 0.7078240 0.0008814147
## 3 target 0.9125082 0.5288205760 0.9387292 0.5332295422
## 4 block:target 0.7209152 0.5277716009 0.7598180 0.5343947151
## p[HF]<.05
## 2 *
## 3
## 4RAEPLTrainedTargetsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.03726626 ±0.64%
## [2] block + participant : 1250.625 ±3.27%
## [3] target + block + participant : 47.47644 ±1.61%
## [4] target + block + target:block + participant : 0.9708311 ±4.7%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.04 0.026
## block 0.60 1.00 834.93
## block:target 0.20 7.47e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of block.
RAEPLTrainedTargetsComparisonMeans()## block emmean SE df lower.CL upper.CL
## baseline 0.467 0.00536 62 0.456 0.477
## first 0.520 0.01689 62 0.486 0.554
## second 0.479 0.00913 62 0.461 0.498
##
## Confidence level used: 0.95RAEPLTrainedTargetsComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Aligned vs. Washout_b1 0.0533 0.0150 62 3.543 0.0023
## Aligned vs. Washout_b2 0.0127 0.0075 62 1.693 0.2866
## Washout_b1 vs. Washout_b2 -0.0406 0.0145 62 -2.807 0.0200
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Aligned vs. Washout_b1 0.16834419
## 2 Aligned vs. Washout_b2 0.04417288
## 3 Washout_b1 vs. Washout_b2 0.11275488RAEPLTrainedTargetsBlockEffectBayesfollowup()## Bayesian t-test aligned vs washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 33.78198 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test aligned vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5299709 ±0.04%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test washout block 1 vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 4.885032 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show that the block effect is driven by the first block of washout trials having larger path lengths than in block 2 or aligned trials. These differences however are small and transient and unlikely to be evidence of aftereffects.
Session 2
In session 2, we tested for retention and generalization across the workspace and hands. As such, the three possible target locations (far, middle, near) were positioned in either quadrant 1 (5°, 45°, or 85° in polar coordinates), quadrant 2 (95°, 135°, or 175° in polar coordinates), or quadrant 4 (275°, 315°, or 355° in polar coordinates), relative to the mirror axis along the vertical midline.
Participants returned after a minimum of three days, and immediately performed 21 trials of mirror reversed reaches to quadrant 1 targets using their dominant or trained hand. They then completed 21 trials of perturbed reaches to quadrant 4 targets followed by 21 trials to quadrant 2 targets. To prevent any possible decay in learning, we had them perform another 21 trials of perturbed reaches to quadrant 1 targets. Finally, we instructed them to switch to their non-dominant hand, and perform 21 trials of perturbed reaches to quadrant 1 targets. The session ended with participants completing 21 washout trials with their non-dominant/ untrained hand.
First, we plot a distribution for when participants returned for the second session.
plotCtrlDaysApart()
## mean: 4.77083333333333 days apart
## sd: 2.52004376298823 days apart
## median: 4 days apartMajority of participants returned after 3 to 4 days (mean = 4.77, SD = 2.52, median = 4 days apart), with a few returning after more than two weeks.
plotOnlineDependentMeasures()
plotBlockedDependentMeasures()
Retention
Amount of compensation
To quantify retention, we compare compensation between the first and last blocks of mirror reversed reaches in session 1 (blocks 1, 26-30), with the first block of mirror reversed reaches in session 2. However, even though we include these analyses here, we note that comparing compensation across the two sessions is confounded, given the quick learning we observe in both sessions.
retentionANOVA()## Retention of learned performance, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 3.0427608 0.05242761 0.009516850
## 3 block 2 94 0.6771262 0.51053561 0.003563209
## 4 target:block 4 188 1.3139291 0.26632176 0.014168800
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.125748932 1.943565e-21 *
## 3 block 0.567565187 2.199694e-06 *
## 4 target:block 0.001038198 1.431477e-61 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 target 0.5335464 0.0848570 0.5357865 0.08467257
## 3 block 0.6981120 0.4607173 0.7128659 0.46360707
## 4 target:block 0.3487819 0.2680358 0.3561359 0.26853030retentionBayesANOVA()## Retention of learned performance, trained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.180781 ±0.79%
## [2] block + participant : 0.05260358 ±0.74%
## [3] target + block + participant : 0.009912509 ±1.56%
## [4] target + block + target:block + participant : 0.00133208 ±1.31%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.15 0.122
## block 0.60 0.05 0.036
## block:target 0.20 1.07e-03 0.004
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no effects of target and block. We note however, that this lack of an effect is likely due to the large inter-participant variability for the near target. Thus, we repeat the analyses with only the far and middle targets.
retentionANOVA(groups=c('far', 'mid'))## Retention of learned performance, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 1 47 0.03733231 0.847622592 0.0001602861
## 3 block 2 94 6.25933389 0.002805434 * 0.0353853407
## 4 target:block 2 94 1.73760131 0.181544973 0.0122848863
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.7532999 0.0014800025 *
## 4 target:block 0.6808462 0.0001445865 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.8021176 0.005557454 * 0.8261044 0.005114167 *
## 4 target:block 0.7580617 0.189711235 0.7780112 0.189130028retentionBayesANOVA(groups=c('far', 'mid'))## Retention of learned performance, trained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.1331974 ±2.84%
## [2] block + participant : 5.780496 ±0.69%
## [3] target + block + participant : 0.7623572 ±2%
## [4] target + block + target:block + participant : 0.2639997 ±1.95%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.15 0.114
## block 0.60 0.86 4.00
## block:target 0.20 0.03 0.138
##
## * Compared among: all models
## * Priors odds: uniform-equalHere, we find a block effect, suggesting that percentages differed across training blocks in session 1 and 2.
retentionComparisonMeans(groups=c('far', 'mid'))## target block emmean SE df lower.CL upper.CL
## far first 46.4 7.46 47 31.4 61.4
## mid first 64.9 12.37 47 40.0 89.8
## far last 87.5 2.78 47 81.9 93.1
## mid last 74.1 5.95 47 62.1 86.1
## far s2_first 58.7 6.79 47 45.0 72.4
## mid s2_first 58.0 12.04 47 33.8 82.3
##
## Confidence level used: 0.95retentionComparisonsEffSize(groups=c('far', 'mid'))## contrast estimate SE df t.ratio p.value
## Session1_B1 vs. Session1_last 25.16 6.89 47 3.650 0.0020
## Session1_B1 vs. Session2_B1 2.71 9.55 47 0.284 1.0000
## Session1_last vs. Session2_B1 -22.45 6.65 47 -3.378 0.0044
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Session1_B1 vs. Session1_last 0.220889059
## 2 Session1_B1 vs. Session2_B1 0.001708071
## 3 Session1_last vs. Session2_B1 0.195356971retentionComparisonsBayesfollowup(groups=c('far', 'mid'))## Bayesian t-test session 1 block 1 vs session 1 last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 42.10735 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test session 1 block 1 vs session 2 block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1628903 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test session 1 last block vs session 2 block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 20.39811 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show that the block effect is driven by a difference between the last block of training in session 1, with both the first blocks of training in the two sessions. Notably, we find no difference between the first blocks in the two sessions.
Completion time
We then compare the completion times across the first and last blocks of mirror reversed reaches in session 1, with the first block of mirror reversed reaches in session 2.
retentionMTANOVA()## Comparing completion times between session 1 and session 2 during learning, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 32.303421 2.098355e-11 * 0.09485507
## 3 block 2 94 48.954649 2.700824e-15 * 0.21315183
## 4 target:block 4 188 8.669581 1.920071e-06 * 0.05843470
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.93454103 2.107476e-01
## 3 block 0.32976089 8.290492e-12 *
## 4 target:block 0.03773864 1.875984e-27 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9385627 7.637153e-11 * 0.9762456 3.457372e-11
## 3 block 0.5987167 4.286371e-10 * 0.6056080 3.487216e-10
## 4 target:block 0.5261101 2.660825e-04 * 0.5513526 2.040060e-04
## p[HF]<.05
## 2 *
## 3 *
## 4 *retentionMTBayesANOVA()## Comparing completion times between session 1 and session 2 during learning, trained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 755556.5 ±0.66%
## [2] block + participant : 4.092589e+19 ±2.56%
## [3] target + block + participant : 5.091651e+27 ±1.57%
## [4] target + block + target:block + participant : 1.937395e+31 ±0.92%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 3.16e+11
## block 0.60 1.00 1.71e+25
## block:target 0.20 1.00 1.52e+04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target x block interaction.
retentionMTComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far first 4.08 0.6183 47 2.84 5.33
## mid first 8.05 0.8367 47 6.37 9.73
## near first 4.32 0.3754 47 3.57 5.08
## far last 1.42 0.0863 47 1.25 1.60
## mid last 2.42 0.1879 47 2.04 2.79
## near last 2.47 0.2086 47 2.05 2.89
## far s2_first 2.22 0.1647 47 1.89 2.55
## mid s2_first 3.67 0.3181 47 3.03 4.31
## near s2_first 2.62 0.2346 47 2.15 3.10
##
## Confidence level used: 0.95retentionMTComparisonsEffSize()## contrast estimate SE df t.ratio
## Far: Session 1 Block 1 vs Session 2 Block 1 -1.865 0.639 47 -2.921
## Far: Session 1 last block vs Session 2 Block 1 0.797 0.148 47 5.373
## Mid: Session 1 Block 1 vs Session 2 Block 1 -4.384 0.861 47 -5.093
## Mid: Session 1 last block vs Session 2 Block 1 1.252 0.321 47 3.905
## Near: Session 1 Block 1 vs Session 2 Block 1 -1.697 0.396 47 -4.285
## Near: Session 1 last block vs Session 2 Block 1 0.157 0.178 47 0.882
## p.value
## 0.0321
## <.0001
## <.0001
## 0.0018
## 0.0005
## 1.0000
##
## P value adjustment: bonferroni method for 6 tests
## contrast etasquared
## 1 Far: Session 1 Block 1 vs Session 2 Block 1 0.15364085
## 2 Far: Session 1 last block vs Session 2 Block 1 0.38048775
## 3 Mid: Session 1 Block 1 vs Session 2 Block 1 0.35557875
## 4 Mid: Session 1 last block vs Session 2 Block 1 0.24494853
## 5 Near: Session 1 Block 1 vs Session 2 Block 1 0.28088338
## 6 Near: Session 1 last block vs Session 2 Block 1 0.01628236retentionMTComparisonsBayesfollowup()## Bayesian t-test Far: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 6.557432 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 7396.022 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3035.037 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 85.27252 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 255.668 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2262132 ±0.05%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show that overall, completion times are slower for the first block of session 2 when compared to the last block of training in session 1. The only exception is the near target, which does not show a difference between these two blocks. However, completion times are faster during the first block of session 2, when compared with the first block of training in session 1. Thus, we do observe partial retention for learning when considering completion times.
Path length
Next, we compare the path lengths across the first and last blocks of mirror reversed reaches in session 1, with the first block of mirror reversed reaches in session 2.
retentionPLANOVA()## Comparing path lengths between session 1 and session 2 during learning, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 19.045316 1.137691e-07 * 0.06016312
## 3 block 2 94 27.018196 5.366485e-10 * 0.13939859
## 4 target:block 4 188 5.947469 1.580018e-04 * 0.04119713
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.96040420 3.948600e-01
## 3 block 0.10857646 6.636212e-23 *
## 4 target:block 0.01761224 1.287306e-34 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9619123 1.849004e-07 * 1.0021212 1.137691e-07
## 3 block 0.5287023 2.555582e-06 * 0.5306124 2.468832e-06
## 4 target:block 0.5277652 3.095080e-03 * 0.5532038 2.630747e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *retentionPLBayesANOVA()## Comparing path lengths between session 1 and session 2 during learning, trained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 3056.949 ±0.74%
## [2] block + participant : 1.166375e+12 ±0.63%
## [3] target + block + participant : 2.917433e+16 ±3.26%
## [4] target + block + target:block + participant : 1.555324e+18 ±1.24%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 9.06e+05
## block 0.60 1.00 3.45e+14
## block:target 0.20 0.98 213.24
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target x block interaction.
retentionPLComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far first 1.380 0.3172 47 0.742 2.019
## mid first 2.412 0.2710 47 1.867 2.957
## near first 1.132 0.1344 47 0.862 1.403
## far last 0.549 0.0273 47 0.494 0.603
## mid last 0.767 0.0384 47 0.690 0.844
## near last 0.706 0.0355 47 0.635 0.777
## far s2_first 0.788 0.0609 47 0.665 0.910
## mid s2_first 1.109 0.0848 47 0.938 1.279
## near s2_first 0.682 0.0381 47 0.606 0.759
##
## Confidence level used: 0.95retentionPLComparisonsEffSize()## contrast estimate SE df t.ratio
## Far: Session 1 Block 1 vs Session 2 Block 1 -0.5927 0.3264 47 -1.816
## Far: Session 1 last block vs Session 2 Block 1 0.2392 0.0566 47 4.228
## Mid: Session 1 Block 1 vs Session 2 Block 1 -1.3036 0.2608 47 -4.998
## Mid: Session 1 last block vs Session 2 Block 1 0.3418 0.0758 47 4.510
## Near: Session 1 Block 1 vs Session 2 Block 1 -0.4501 0.1335 47 -3.371
## Near: Session 1 last block vs Session 2 Block 1 -0.0237 0.0422 47 -0.562
## p.value
## 0.4544
## 0.0006
## 0.0001
## 0.0003
## 0.0090
## 1.0000
##
## P value adjustment: bonferroni method for 6 tests
## contrast etasquared
## 1 Far: Session 1 Block 1 vs Session 2 Block 1 0.065576655
## 2 Far: Session 1 last block vs Session 2 Block 1 0.275547535
## 3 Mid: Session 1 Block 1 vs Session 2 Block 1 0.347030519
## 4 Mid: Session 1 last block vs Session 2 Block 1 0.302062210
## 5 Near: Session 1 Block 1 vs Session 2 Block 1 0.194659415
## 6 Near: Session 1 last block vs Session 2 Block 1 0.006682688retentionPLComparisonsBayesfollowup()## Bayesian t-test Far: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7138299 ±0.03%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 216.4437 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2253.822 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 501.5245 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 20.00483 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1821098 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show path lengths were slightly longer during the first block of session 2 when compared with the last block of training in session 1, except for the near target. Path lengths, however, are shorter during session 2 block 1, when compared with the first block of training in session 1, although this did not reach significance for the far target. Taken together, path lengths show the same pattern of results as in completion time, where we observe partial retention of learning.
Generalization across the workspace
Amount of compensation
To quantify generalization, we compare compensation across quadrants in session 2. We conduct a 3x3 (target x block) within-subjects ANOVA to compare the first and last blocks of reaches to quadrant 1 with the first block of reaches in quadrant 4 (test targets on same side of mirror axis). We repeat this test but instead compare quadrant 1 with quadrant 2 (test targets on opposite side of axis). Again, although we report them here, we note that comparisons are confounded for compensation values.
#Quadrant 1 vs Quadrant 4
learningANOVA2Quads(quadrantA= '1', quadrantB = '4')##
## Quadrants 1 and 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 3.1112559 0.04916328 * 0.013556430
## 3 block 2 94 1.0906539 0.34021013 0.005422759
## 4 target:block 4 188 0.4258092 0.78988983 0.003879238
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.095746312 3.679657e-24 *
## 3 block 0.928683474 1.823717e-01
## 4 target:block 0.003811174 3.847872e-49 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 target 0.5251401 0.08213998 0.5268090 0.0820005
## 3 block 0.9334309 0.33709576 0.9705659 0.3388795
## 4 target:block 0.4708650 0.64250688 0.4898762 0.6504108learningBayesANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.4588984 ±0.69%
## [2] block + participant : 0.106279 ±23.96%
## [3] target + block + participant : 0.0368885 ±1.95%
## [4] target + block + target:block + participant : 0.0008188149 ±1.14%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.31 0.299
## block 0.60 0.09 0.066
## block:target 0.20 5.11e-04 0.002
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Quadrant 2
learningANOVA2Quads(quadrantA= '1', quadrantB = '2')##
## Quadrants 1 and 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 0.76847253 0.4666118 0.0039237268
## 3 block 2 94 0.42961777 0.6520291 0.0020014306
## 4 target:block 4 188 0.05851064 0.9936073 0.0004963363
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.05856517 4.525913e-29 *
## 3 block 0.94053518 2.441328e-01
## 4 target:block 0.00632774 2.579651e-44 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 target 0.5150830 0.3886905 0.5160772 0.3889202
## 3 block 0.9438728 0.6405395 0.9821255 0.6484419
## 4 target:block 0.4854642 0.9392744 0.5060635 0.9447603learningBayesANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.05877051 ±0.62%
## [2] block + participant : 0.03918068 ±0.71%
## [3] target + block + participant : 0.002274136 ±0.93%
## [4] target + block + target:block + participant : 2.8964e-05 ±1.42%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.06 0.039
## block 0.60 0.04 0.026
## block:target 0.20 2.63e-05 1.05e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no effects of target or block. However, this could again be confounded by the large inter-participant variability for the near target. We repeat the analyses for only the far and middle targets.
#Quadrant 1 vs Quadrant 4
learningANOVA2Quads(groups = c('far', 'mid'), quadrantA= '1', quadrantB = '4')##
## Quadrants 1 and 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 1 47 1.5087350 0.225447702 0.006080462
## 3 block 2 94 5.1777091 0.007358749 * 0.031667561
## 4 target:block 2 94 0.4596672 0.632905630 0.002971714
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9260359 0.17078097
## 4 target:block 0.8587318 0.03011087 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9311298 0.008816806 * 0.9680199 0.008002675 *
## 4 target:block 0.8762182 0.607477293 0.9074185 0.614203326learningBayesANOVA2Quads(groups = c('far', 'mid'), quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.3118929 ±1.1%
## [2] block + participant : 3.680452 ±0.6%
## [3] target + block + participant : 1.165895 ±1.26%
## [4] target + block + target:block + participant : 0.1329012 ±8.86%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.26 0.229
## block 0.60 0.79 2.53
## block:target 0.20 0.02 0.086
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Quadrant 2
learningANOVA2Quads(groups = c('far', 'mid'), quadrantA= '1', quadrantB = '2')##
## Quadrants 1 and 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 1 47 1.205592 0.27780025 0.003593097
## 3 block 2 94 3.281914 0.04190297 * 0.023296255
## 4 target:block 2 94 0.380620 0.68448598 0.002855900
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9772915 0.5895960
## 4 target:block 0.9135719 0.1250498
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9777957 0.04305723 * 1.0197535 0.04190297 *
## 4 target:block 0.9204475 0.66723546 0.9562076 0.67517520learningBayesANOVA2Quads(groups = c('far', 'mid'), quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.2134176 ±1.36%
## [2] block + participant : 0.9850109 ±0.9%
## [3] target + block + participant : 0.2117372 ±2.16%
## [4] target + block + target:block + participant : 0.02150111 ±3.4%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.18 0.150
## block 0.60 0.50 0.669
## block:target 0.20 8.84e-03 0.036
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a block effect for both tests conducted.
QAandBComparisonMeans(quadrantA = '1', quadrantB = '4')## block emmean SE df lower.CL upper.CL
## first 58.4 6.08 47 46.1 70.6
## last 80.0 6.01 47 67.9 92.1
## qb_first 80.9 5.82 47 69.2 92.6
##
## Confidence level used: 0.95QAandBComparisonsEffSize(quadrantA = '1', quadrantB = '4')## contrast estimate SE df t.ratio p.value
## Quad A block 1 vs. Quad A last block 21.635 8.24 47 2.625 0.0350
## Quad A block 1 vs. Quad B block 1 22.546 8.63 47 2.611 0.0362
## Quad A last block vs. Quad B block 1 0.911 6.80 47 0.134 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Quad A block 1 vs. Quad A last block 0.1278360797
## 2 Quad A block 1 vs. Quad B block 1 0.1266837983
## 3 Quad A last block vs. Quad B block 1 0.0003820331QAandBComparisonsBayesfollowup(quadrantA = '1', quadrantB = '4')## Bayesian t-test Quad A block 1 vs. Quad A last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.343568 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.246058 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1581341 ±0.07%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSIn comparing reaches to quadrant 1 and quadrant 4 (test targets on the same side but lower on the workspace than training targets), we find no differences between the last block of reaches in the training quadrant and the first block of of reaches to the test quadrant. Both of these quadrants also differed from the first block of reaches to the training quadrant. This suggests generalization of learning to the test quadrant.
QAandBComparisonMeans(quadrantA = '1', quadrantB = '2')## block emmean SE df lower.CL upper.CL
## first 58.4 6.08 47 46.1 70.6
## last 80.0 6.01 47 67.9 92.1
## qb_first 63.7 6.45 47 50.7 76.6
##
## Confidence level used: 0.95QAandBComparisonsEffSize(quadrantA = '1', quadrantB = '2')## contrast estimate SE df t.ratio p.value
## Quad A block 1 vs. Quad A last block 21.64 8.24 47 2.625 0.0350
## Quad A block 1 vs. Quad B block 1 5.32 9.38 47 0.567 1.0000
## Quad A last block vs. Quad B block 1 -16.32 8.74 47 -1.867 0.2043
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Quad A block 1 vs. Quad A last block 0.127836080
## 2 Quad A block 1 vs. Quad B block 1 0.006785903
## 3 Quad A last block vs. Quad B block 1 0.069072042QAandBComparisonsBayesfollowup(quadrantA = '1', quadrantB = '2')## Bayesian t-test Quad A block 1 vs. Quad A last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.343568 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1825328 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7762621 ±0.03%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWhen switching to targets on quadrant 2 (test targets on the opposite side of the mirror axis), we find no differences between the first block of reaches to the test quadrant with both first and last blocks of reaches to the training quadrant.
Completion time
We then compare completion time across quadrants. We conduct a 3x3 (target x block) within-subjects ANOVA to compare the first set of reaches to quadrant 1 with reaches in quadrant 4. We repeat this test but instead compare quadrant 1 with quadrant 2.
#Quadrant 1 vs Quadrant 4
MTANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 34.878329 4.673665e-12 * 0.09853368
## 3 block 2 94 25.061617 1.890214e-09 * 0.08841968
## 4 target:block 4 188 5.119601 6.153438e-04 * 0.02933923
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9323575 0.1997085191
## 3 block 0.8272060 0.0127383915 *
## 4 target:block 0.4759989 0.0001013938 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9366431 1.942682e-11 * 0.9741208 8.362336e-12
## 3 block 0.8526647 2.210200e-08 * 0.8815144 1.364840e-08
## 4 target:block 0.7202684 2.513877e-03 * 0.7722963 1.931490e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *MTBayesANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 2867452254 ±0.69%
## [2] block + participant : 131449840 ±0.97%
## [3] target + block + participant : 1.23231e+19 ±1.44%
## [4] target + block + target:block + participant : 2.662971e+20 ±6.48%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.41e+12
## block 0.60 1.00 6.48e+10
## block:target 0.20 0.96 86.44
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Quadrant 2
MTANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 10.987863 5.149387e-05 * 0.05538502
## 3 block 2 94 15.045635 2.143736e-06 * 0.04617133
## 4 target:block 4 188 2.789836 2.773545e-02 * 0.01736813
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.42471928 2.794766e-09 *
## 3 block 0.78803295 4.173694e-03 *
## 4 target:block 0.05029992 9.039516e-25 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.6348075 6.784198e-04 * 0.6444459 6.335123e-04
## 3 block 0.8251049 1.230914e-05 * 0.8512727 9.471579e-06
## 4 target:block 0.4098043 7.790029e-02 0.4226251 7.618370e-02
## p[HF]<.05
## 2 *
## 3 *
## 4MTBayesANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 18085.67 ±0.67%
## [2] block + participant : 1581.3 ±0.86%
## [3] target + block + participant : 65180538 ±2.06%
## [4] target + block + target:block + participant : 32594106 ±1.31%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 4.12e+04
## block 0.60 1.00 3.60e+03
## block:target 0.20 0.33 2.00
##
## * Compared among: all models
## * Priors odds: uniform-equalIn comparing quadrants 1 and 4, We find a significant target x block interaction.
quadrant1and4MTComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far first 2.22 0.1647 47 1.89 2.55
## mid first 3.67 0.3181 47 3.03 4.31
## near first 2.62 0.2346 47 2.15 3.10
## far last 1.27 0.0885 47 1.09 1.45
## mid last 1.87 0.1177 47 1.63 2.10
## near last 2.22 0.1927 47 1.84 2.61
## far qb_first 1.61 0.1548 47 1.30 1.92
## mid qb_first 2.84 0.2445 47 2.35 3.34
## near qb_first 2.46 0.1927 47 2.08 2.85
##
## Confidence level used: 0.95Q1and4MTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Far: Quad A block 1 vs. Quad B block 1 -0.611 0.196 47 -3.120 0.0185
## Far: Quad A last block vs. Quad B block 1 0.340 0.151 47 2.245 0.1770
## Mid: Quad A block 1 vs. Quad B block 1 -0.824 0.359 47 -2.297 0.1569
## Mid: Quad A last block vs. Quad B block 1 0.978 0.250 47 3.917 0.0017
## Near: Quad A block 1 vs. Quad B block 1 -0.159 0.242 47 -0.656 1.0000
## Near: Quad A last block vs. Quad B block 1 0.241 0.183 47 1.319 1.0000
##
## P value adjustment: bonferroni method for 6 tests
## contrast etasquared
## 1 Far: Quad A block 1 vs. Quad B block 1 0.171544216
## 2 Far: Quad A last block vs. Quad B block 1 0.096863739
## 3 Mid: Quad A block 1 vs. Quad B block 1 0.100893540
## 4 Mid: Quad A last block vs. Quad B block 1 0.246102055
## 5 Near: Quad A block 1 vs. Quad B block 1 0.009075564
## 6 Near: Quad A last block vs. Quad B block 1 0.035693667Q1and4MTComparisonsBayesfollowup()## Bayesian t-test Far: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 10.59562 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.529839 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.690994 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 88.25763 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1921862 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3531015 ±0.04%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSOn average, completion times during the first block of the test quadrant are shorter compared to the first block of reaches to the training quadrant.
In comparing quadrants 1 and 2, We find a significant block effect
quadrant1and2MTComparisonMeans()## block emmean SE df lower.CL upper.CL
## first 2.84 0.193 47 2.45 3.22
## last 1.79 0.105 47 1.57 2.00
## qb_first 2.26 0.248 47 1.77 2.76
##
## Confidence level used: 0.95Q1and2MTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Quad A block 1 vs. Quad A last block -1.050 0.145 47 -7.268 <.0001
## Quad A block 1 vs. Quad B block 1 -0.573 0.199 47 -2.879 0.0180
## Quad A last block vs. Quad B block 1 0.477 0.223 47 2.139 0.1130
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Quad A block 1 vs. Quad A last block 0.52918173
## 2 Quad A block 1 vs. Quad B block 1 0.14990805
## 3 Quad A last block vs. Quad B block 1 0.08870736Q1and2MTComparisonsBayesfollowup()## Bayesian t-test Quad A block 1 vs. Quad A last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3715860 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5.940946 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.250884 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show that the first block in quadrant 2 does not differ from the last block of quadrant 1.
Path length
Next, we compare path length across quadrants. We conduct a 3x3 (target x block) within-subjects ANOVA to compare the first and last blocks of reaches to quadrant 1 with the first block of reaches reaches in quadrant 4. We repeat this test but instead compare quadrant 1 with quadrant 2.
#Quadrant 1 vs Quadrant 4
PLANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 29.869865 9.079499e-11 * 0.09605367
## 3 block 2 94 22.486797 1.045181e-08 * 0.06539614
## 4 target:block 4 188 5.128782 6.061229e-04 * 0.04180922
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9335704 2.057701e-01
## 3 block 0.9716948 5.166394e-01
## 4 target:block 0.3343204 1.224874e-07 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9377084 3.079637e-10 * 0.9752999 1.473434e-10
## 3 block 0.9724740 1.580708e-08 * 1.0138430 1.045181e-08
## 4 target:block 0.7009076 2.743099e-03 * 0.7499160 2.137931e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *PLBayesANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 123464473 ±0.86%
## [2] block + participant : 41251.23 ±0.75%
## [3] target + block + participant : 3.163e+13 ±1.65%
## [4] target + block + target:block + participant : 4.470611e+15 ±12.59%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 7.28e+10
## block 0.60 1.00 2.43e+07
## block:target 0.20 0.99 565.36
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Quadrant 2
PLANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 13.109122 9.514834e-06 * 0.05460617
## 3 block 2 94 22.059952 1.396254e-08 * 0.07137449
## 4 target:block 4 188 6.600672 5.429097e-05 * 0.04585673
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.8601959 3.131403e-02 *
## 3 block 0.9679317 4.725284e-01
## 4 target:block 0.4097668 6.220397e-06 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.8773437 2.729690e-05 * 0.9086576 2.084996e-05
## 3 block 0.9689281 2.208167e-08 * 1.0099064 1.396254e-08
## 4 target:block 0.7211825 4.091593e-04 * 0.7733548 2.797956e-04
## p[HF]<.05
## 2 *
## 3 *
## 4 *PLBayesANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 5193.948 ±1.42%
## [2] block + participant : 367207.7 ±1.14%
## [3] target + block + participant : 5825296451 ±1.89%
## [4] target + block + target:block + participant : 1.943335e+12 ±1.52%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 3.54e+06
## block 0.60 1.00 2.50e+08
## block:target 0.20 1.00 1.33e+03
##
## * Compared among: all models
## * Priors odds: uniform-equalIn both tests, we find a significant target x block interaction.
quadrantA1andBPLComparisonMeans(quadrantA='1', quadrantB='4')## target block emmean SE df lower.CL upper.CL
## far first 0.788 0.0609 47 0.665 0.910
## mid first 1.109 0.0848 47 0.938 1.279
## near first 0.682 0.0381 47 0.606 0.759
## far last 0.480 0.0204 47 0.439 0.521
## mid last 0.673 0.0476 47 0.578 0.769
## near last 0.697 0.0837 47 0.529 0.866
## far qb_first 0.530 0.0288 47 0.472 0.588
## mid qb_first 0.900 0.0669 47 0.766 1.035
## near qb_first 0.637 0.0316 47 0.573 0.700
##
## Confidence level used: 0.95QAandBPLComparisonsEffSize(quadrantA='1', quadrantB='4')## contrast estimate SE df t.ratio p.value
## Far: Quad A block 1 vs. Quad B block 1 -0.2575 0.0700 47 -3.679 0.0036
## Far: Quad A last block vs. Quad B block 1 0.0502 0.0323 47 1.552 0.7642
## Mid: Quad A block 1 vs. Quad B block 1 -0.2086 0.0978 47 -2.132 0.2295
## Mid: Quad A last block vs. Quad B block 1 0.2267 0.0770 47 2.945 0.0301
## Near: Quad A block 1 vs. Quad B block 1 -0.0455 0.0487 47 -0.934 1.0000
## Near: Quad A last block vs. Quad B block 1 -0.0604 0.0744 47 -0.812 1.0000
##
## P value adjustment: bonferroni method for 6 tests
## contrast etasquared
## 1 Far: Quad A block 1 vs. Quad B block 1 0.22360089
## 2 Far: Quad A last block vs. Quad B block 1 0.04875087
## 3 Mid: Quad A block 1 vs. Quad B block 1 0.08818897
## 4 Mid: Quad A last block vs. Quad B block 1 0.15577498
## 5 Near: Quad A block 1 vs. Quad B block 1 0.01823133
## 6 Near: Quad A last block vs. Quad B block 1 0.01383454QAandBPLComparisonsBayesfollowup(quadrantA='1', quadrantB='4')## Bayesian t-test Far: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 45.54181 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4789082 ±0.04%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.235059 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 6.93962 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2364588 ±0.05%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2139991 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSOn average, path lengths are shorter for the first block of reaches to the test quadrant, compared to the first block of reaches to the training quadrant.
quadrantA1andBPLComparisonMeans(quadrantA='1', quadrantB='2')## target block emmean SE df lower.CL upper.CL
## far first 0.788 0.0609 47 0.665 0.910
## mid first 1.109 0.0848 47 0.938 1.279
## near first 0.682 0.0381 47 0.606 0.759
## far last 0.480 0.0204 47 0.439 0.521
## mid last 0.673 0.0476 47 0.578 0.769
## near last 0.697 0.0837 47 0.529 0.866
## far qb_first 0.613 0.0400 47 0.533 0.693
## mid qb_first 0.736 0.0413 47 0.653 0.819
## near qb_first 0.658 0.0422 47 0.573 0.743
##
## Confidence level used: 0.95QAandBPLComparisonsEffSize(quadrantA='1', quadrantB='2')## contrast estimate SE df t.ratio p.value
## Far: Quad A block 1 vs. Quad B block 1 -0.1748 0.0725 47 -2.412 0.1189
## Far: Quad A last block vs. Quad B block 1 0.1329 0.0458 47 2.900 0.0340
## Mid: Quad A block 1 vs. Quad B block 1 -0.3726 0.0720 47 -5.175 <.0001
## Mid: Quad A last block vs. Quad B block 1 0.0626 0.0482 47 1.300 1.0000
## Near: Quad A block 1 vs. Quad B block 1 -0.0244 0.0516 47 -0.473 1.0000
## Near: Quad A last block vs. Quad B block 1 -0.0393 0.0811 47 -0.485 1.0000
##
## P value adjustment: bonferroni method for 6 tests
## contrast etasquared
## 1 Far: Quad A block 1 vs. Quad B block 1 0.110163925
## 2 Far: Quad A last block vs. Quad B block 1 0.151734852
## 3 Mid: Quad A block 1 vs. Quad B block 1 0.362999475
## 4 Mid: Quad A last block vs. Quad B block 1 0.034734348
## 5 Near: Quad A block 1 vs. Quad B block 1 0.004733487
## 6 Near: Quad A last block vs. Quad B block 1 0.004985638QAandBPLComparisonsBayesfollowup(quadrantA='1', quadrantB='2')## Bayesian t-test Far: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.132898 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 6.234701 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3942.651 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3453413 ±0.04%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Quad A block 1 vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1743107 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Quad A last block vs. Quad B block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1752996 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSAgain, on average, path lengths are shorter for the first block of reaches to the test quadrant, compared to the first block of reaches to the training quadrant.
Generalization to the untrained hand
Amount of compensation
We conduct tests comparing compensation from the first block of reaches with the untrained hand, to the first and last block of reaches in session 1.
intermanualANOVA(groups=c('far','mid'))## Transfer of learned performance to untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 1 47 0.01316992 0.9091240019 7.579234e-05
## 3 block 2 94 8.13664199 0.0005506868 * 4.236988e-02
## 4 target:block 2 94 2.78151626 0.0670498279 1.336899e-02
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8698297 0.04045638 *
## 4 target:block 0.9436190 0.26322270
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8848224 0.0009662042 * 0.9168947 0.0008259926
## 4 target:block 0.9466281 0.0702487647 0.9851775 0.0679241195
## p[HF]<.05
## 3 *
## 4intermanualBayesANOVA(groups=c('far','mid'))## Transfer of learned performance to untrained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.1281271 ±1.22%
## [2] block + participant : 21.87424 ±0.8%
## [3] target + block + participant : 2.691551 ±1.08%
## [4] target + block + target:block + participant : 1.19105 ±1.62%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.15 0.117
## block 0.60 0.96 15.22
## block:target 0.20 0.04 0.185
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a block effect.
intermanualComparisonsEffSize(groups=c('far','mid'))## contrast estimate SE df t.ratio p.value
## Session1_B1 vs. Session1_last 25.2 6.89 47 3.650 0.0020
## Session1_B1 vs. Session2_B1 -3.1 8.96 47 -0.346 1.0000
## Session1_last vs. Session2_B1 -28.3 7.02 47 -4.024 0.0006
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Session1_B1 vs. Session1_last 0.220889059
## 2 Session1_B1 vs. Session2_B1 0.002546269
## 3 Session1_last vs. Session2_B1 0.256286833intermanualComparisonsBayesfollowup(groups=c('far','mid'))## Bayesian t-test session 1 block 1 vs session 1 last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 42.10735 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test session 1 block 1 vs session 2 block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1659737 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test session 1 last block vs session 2 block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 119.8714 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWe find higher compensation values for the last block of training in session 1, compared to the other two blocks.
Completion time
We also compare completion times in the first block of reaches with the untrained hand to the first and last block of reaches during training in session 1.
intermanualMTANOVA()## Transfer of learned performance to untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 25.331068 1.586098e-09 * 0.08606339
## 3 block 2 94 47.562466 5.368047e-15 * 0.22399511
## 4 target:block 4 188 9.866698 2.876280e-07 * 0.06231317
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.8476693 2.234643e-02 *
## 3 block 0.4123327 1.414814e-09 *
## 4 target:block 0.1056077 6.536393e-18 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.8678064 1.472495e-08 * 0.8981610 8.823242e-09
## 3 block 0.6298549 2.614195e-10 * 0.6391091 1.994304e-10
## 4 target:block 0.5705020 5.403870e-05 * 0.6011920 3.705316e-05
## p[HF]<.05
## 2 *
## 3 *
## 4 *intermanualMTBayesANOVA()## Transfer of learned performance to untrained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 79481.11 ±0.85%
## [2] block + participant : 3.203433e+20 ±0.68%
## [3] target + block + participant : 2.527085e+27 ±1.06%
## [4] target + block + target:block + participant : 1.610329e+31 ±1.34%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 3.35e+10
## block 0.60 1.00 1.35e+26
## block:target 0.20 1.00 2.55e+04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target X block interaction.
intermanualMTComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far first 4.08 0.6183 47 2.84 5.33
## mid first 8.05 0.8367 47 6.37 9.73
## near first 4.32 0.3754 47 3.57 5.08
## far last 1.42 0.0863 47 1.25 1.60
## mid last 2.42 0.1879 47 2.04 2.79
## near last 2.47 0.2086 47 2.05 2.89
## far s2_first 2.16 0.2341 47 1.68 2.63
## mid s2_first 3.22 0.3121 47 2.59 3.85
## near s2_first 2.30 0.1698 47 1.96 2.65
##
## Confidence level used: 0.95intermanualMTComparisonsEffSize()## contrast estimate SE df t.ratio
## Far: Session 1 Block 1 vs Session 2 Block 1 -1.929 0.665 47 -2.901
## Far: Session 1 last block vs Session 2 Block 1 0.733 0.244 47 3.006
## Mid: Session 1 Block 1 vs Session 2 Block 1 -4.833 0.831 47 -5.819
## Mid: Session 1 last block vs Session 2 Block 1 0.802 0.326 47 2.460
## Near: Session 1 Block 1 vs Session 2 Block 1 -2.016 0.393 47 -5.130
## Near: Session 1 last block vs Session 2 Block 1 -0.162 0.171 47 -0.945
## p.value
## 0.0339
## 0.0254
## <.0001
## 0.1057
## <.0001
## 1.0000
##
## P value adjustment: bonferroni method for 6 tests
## contrast etasquared
## 1 Far: Session 1 Block 1 vs Session 2 Block 1 0.15185710
## 2 Far: Session 1 last block vs Session 2 Block 1 0.16127209
## 3 Mid: Session 1 Block 1 vs Session 2 Block 1 0.41875203
## 4 Mid: Session 1 last block vs Session 2 Block 1 0.11409467
## 5 Near: Session 1 Block 1 vs Session 2 Block 1 0.35898428
## 6 Near: Session 1 last block vs Session 2 Block 1 0.01865694intermanualMTComparisonsBayesfollowup()## Bayesian t-test Far: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 6.254894 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 8.035279 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 31280.47 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.355317 ±0.01%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3420.912 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2387601 ±0.05%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSOverall, we find that reaches using the untrained hand are faster than initial reaches in session 1 training. But, these are generally slower than reaches during the last block of training in session 1. This suggests partial retention.
Path length
We also compare the first block of reaches with the untrained hand to the first and last block of reaches during training in session 1.
intermanualPLANOVA()## Transfer of learned performance to untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 16.504773 7.189523e-07 * 0.05706883
## 3 block 2 94 23.828872 4.253182e-09 * 0.14177073
## 4 target:block 4 188 6.569794 5.709626e-05 * 0.04201766
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.99386801 8.680813e-01
## 3 block 0.21383187 3.905405e-16 *
## 4 target:block 0.02674874 1.110003e-30 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9939054 7.688015e-07 * 1.0376624 7.189523e-07
## 3 block 0.5598577 4.791492e-06 * 0.5639278 4.488294e-06
## 4 target:block 0.5254604 1.770502e-03 * 0.5506262 1.472048e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *intermanualPLBayesANOVA()## Transfer of learned performance to untrained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 1209.647 ±0.84%
## [2] block + participant : 1.013654e+12 ±0.75%
## [3] target + block + participant : 8.025682e+15 ±1.78%
## [4] target + block + target:block + participant : 3.966276e+17 ±1.54%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 2.66e+05
## block 0.60 1.00 2.23e+14
## block:target 0.20 0.98 197.65
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target X block interaction.
intermanualPLComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far first 1.380 0.3172 47 0.742 2.019
## mid first 2.412 0.2710 47 1.867 2.957
## near first 1.132 0.1344 47 0.862 1.403
## far last 0.549 0.0273 47 0.494 0.603
## mid last 0.767 0.0384 47 0.690 0.844
## near last 0.706 0.0355 47 0.635 0.777
## far s2_first 0.725 0.0683 47 0.588 0.862
## mid s2_first 1.056 0.0776 47 0.900 1.212
## near s2_first 0.717 0.0444 47 0.627 0.806
##
## Confidence level used: 0.95intermanualPLComparisonsEffSize()## contrast estimate SE df t.ratio
## Far: Session 1 Block 1 vs Session 2 Block 1 -0.6556 0.3295 47 -1.990
## Far: Session 1 last block vs Session 2 Block 1 0.1763 0.0774 47 2.279
## Mid: Session 1 Block 1 vs Session 2 Block 1 -1.3565 0.2670 47 -5.080
## Mid: Session 1 last block vs Session 2 Block 1 0.2888 0.0768 47 3.760
## Near: Session 1 Block 1 vs Session 2 Block 1 -0.4156 0.1450 47 -2.866
## Near: Session 1 last block vs Session 2 Block 1 0.0107 0.0483 47 0.222
## p.value
## 0.3147
## 0.1637
## <.0001
## 0.0028
## 0.0372
## 1.0000
##
## P value adjustment: bonferroni method for 6 tests
## contrast etasquared
## 1 Far: Session 1 Block 1 vs Session 2 Block 1 0.077698776
## 2 Far: Session 1 last block vs Session 2 Block 1 0.099472141
## 3 Mid: Session 1 Block 1 vs Session 2 Block 1 0.354453562
## 4 Mid: Session 1 last block vs Session 2 Block 1 0.231211462
## 5 Near: Session 1 Block 1 vs Session 2 Block 1 0.148793874
## 6 Near: Session 1 last block vs Session 2 Block 1 0.001050348intermanualPLComparisonsBayesfollowup()## Bayesian t-test Far: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.9560596 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.632214 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2917.777 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 56.83703 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 Block 1 vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5.768924 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 last block vs Session 2 Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1605128 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSOverall, we find that reaches using the untrained hand are shorter than initial reaches in session 1 training. But, these are generally longer than reaches during the last block of training in session 1. This suggests partial retention.
Reach aftereffects for the untrained/ nondominant hand
Amount of compensation
First, we test for target or block effects for compensation within washout trials using the nondominant or untrained hand.
washoutLearningANOVA()## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 15.1220397 2.023257e-06 * 0.042833644
## 3 target 2 94 3.5808510 3.171401e-02 * 0.017107267
## 4 block:target 4 188 0.8966133 4.670917e-01 0.008680658
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.9057849 0.10270157
## 3 target 0.8426683 0.01950308 *
## 4 block:target 0.7970306 0.32682005
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.9138971 4.800909e-06 * 0.9489699 3.375679e-06
## 3 target 0.8640565 3.856491e-02 * 0.8940364 3.693677e-02
## 4 block:target 0.8950415 4.585455e-01 0.9779399 4.653805e-01
## p[HF]<.05
## 2 *
## 3 *
## 4washoutLearningBayesANOVA()## Quadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.9479374 ±0.7%
## [2] block + participant : 345.8017 ±0.94%
## [3] target + block + participant : 386.0219 ±1.13%
## [4] target + block + target:block + participant : 22.04452 ±1.54%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.54 0.786
## block 0.60 1.00 258.01
## block:target 0.20 0.03 0.120
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find main effects of block and target, but no interaction. In the Bayesian test, we only find the effect of block.
washoutComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## block 1 vs. block 2 -22.43 4.82 47 -4.656 0.0001
## block 1 vs. block 3 -25.00 5.69 47 -4.394 0.0002
## block 2 vs. block 3 -2.57 4.41 47 -0.584 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 block 1 vs. block 2 0.315654642
## 2 block 1 vs. block 3 0.291160194
## 3 block 2 vs. block 3 0.007194419washoutComparisonsBayesfollowup()## Bayesian t-test block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 781.4781 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 353.6289 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test block 2 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1842172 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show that the effect of block is driven by the difference of the first block of washout trials with the other blocks. This confirms what we see in the plot, where initially participants are compensating in the first washout trial. However, this is likely due to task switching rather than aftereffects, as participants were not instructed that the perturbation has been turned off.
washoutTargetEffectComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 4.42 7.50 47 0.589 1.0000
## Far vs. Near -12.14 6.21 47 -1.956 0.1693
## Mid vs. Near -16.56 5.33 47 -3.108 0.0096
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.007324856
## 2 Far vs. Near 0.075266800
## 3 Mid vs. Near 0.170452381washoutTargetEffectComparisonsBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1847585 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.9013441 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 10.28693 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests on the target effect show that the middle target differs from the near target.
Then, we compare the first and second blocks of washout trials with the last block of aligned baseline trials using the nondominant hand from the first session. We conduct a 2X3 (target x block) within-subjects ANOVA.
RAEUntrainedHandANOVA(groups=c('far','mid'))## Comparing angular reach deviations during washout trials with aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 1 47 0.05941554 0.808482955 0.0002171446
## 3 block 2 94 7.22534568 0.001205285 * 0.0438707333
## 4 target:block 2 94 0.31052030 0.733814487 0.0027348275
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9376207 0.2273136
## 4 target:block 0.9599458 0.3905483
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9412834 0.001540764 * 0.9792579 0.001314429 *
## 4 target:block 0.9614884 0.725301833 1.0016509 0.733814487RAEUntrainedHandBayesANOVA(groups=c('far','mid'))## Comparing percent of comepensation during washout trials with aligned trials across targets and blocks, untrained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.1336219 ±1.96%
## [2] block + participant : 16.71674 ±0.75%
## [3] target + block + participant : 2.227154 ±1.84%
## [4] target + block + target:block + participant : 0.2161091 ±2.27%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.13 0.097
## block 0.60 0.94 11.27
## block:target 0.20 0.01 0.043
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of block.
untrainedHandSessionComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Baseline last block vs. Washout block 1 22.3 7.47 47 2.991 0.0133
## Baseline last block vs. Washout block 2 -2.3 6.21 47 -0.370 1.0000
## Washout block 1 vs. Washout block 2 -24.6 7.70 47 -3.197 0.0074
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Baseline last block vs. Washout block 1 0.159870408
## 2 Baseline last block vs. Washout block 2 0.002908011
## 3 Washout block 1 vs. Washout block 2 0.178642999untrainedHandSessionComparisonsBayesfollowup()## Bayesian t-test Baseline last block vs Washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 7.739744 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Baseline last block vs Washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1673232 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Washout block 1 vs Washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 12.85403 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSWe find that the last block of baseline and the second washout block differ from the first block of washout. This is evident with how participants’ reaches were deviated during the first trial of washout. However, the absence of deviations by the second trial suggest that there are no aftereffects. Deviations from the first trial are only due to directly switching tasks between perturbed and aligned trials without any breaks in between.
Completion time
We compare completion times during the first two blocks of session 2 washout with those during the last block of aligned reaches using the nondominant hand in session 1. We conduct a 3x3 (target x block) within-subjects ANOVA.
RAEUntrainedHandMTANOVA()## Comparing completion times during washout trials with aligned trials across targets and blocks, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 4.032945 2.087468e-02 * 0.01325056
## 3 block 2 94 40.988440 1.587067e-13 * 0.10446644
## 4 target:block 4 188 5.798489 2.017223e-04 * 0.03612509
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.74970827 1.325937e-03 *
## 3 block 0.82688621 1.262560e-02 *
## 4 target:block 0.09996314 2.049144e-18 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.7998133 2.975579e-02 * 0.8235844 2.852826e-02
## 3 block 0.8524322 7.145038e-12 * 0.8812590 3.394311e-12
## 4 target:block 0.5211860 3.702938e-03 * 0.5458486 3.180458e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *RAEUntrainedHandMTBayesANOVA()## Comparing completion times during washout trials with aligned trials across targets and blocks, untrained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.6439843 ±1.81%
## [2] block + participant : 452528327422 ±0.83%
## [3] target + block + participant : 504553770054 ±1.33%
## [4] target + block + target:block + participant : 8.587656e+13 ±3.09%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.99 127.26
## block 0.60 1.00 3.52e+13
## block:target 0.20 0.99 358.91
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a target X block interaction.
RAEUntrainedHandMTComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far s1_last 1.085 0.0823 47 0.920 1.25
## mid s1_last 0.988 0.0745 47 0.838 1.14
## near s1_last 1.143 0.0832 47 0.976 1.31
## far first 1.246 0.0908 47 1.064 1.43
## mid first 1.874 0.1692 47 1.534 2.21
## near first 1.545 0.1297 47 1.284 1.81
## far second 1.027 0.0598 47 0.907 1.15
## mid second 1.052 0.0765 47 0.898 1.21
## near second 1.086 0.0771 47 0.931 1.24
##
## Confidence level used: 0.95RAEUntrainedHandMTComparisonsEffSize()## contrast estimate SE df t.ratio
## Far: Session 1 last block vs washout block 1 0.1612 0.1002 47 1.608
## Far: Session 1 last block vs washout block 2 -0.0583 0.0742 47 -0.786
## Far: washout block 1 vs washout block 2 -0.2195 0.0871 47 -2.521
## Mid: Session 1 last block vs washout block 1 0.8860 0.1500 47 5.906
## Mid: Session 1 last block vs washout block 2 0.0639 0.0808 47 0.790
## Mid: washout block 1 vs washout block 2 -0.8222 0.1324 47 -6.211
## Near: Session 1 last block vs washout block 1 0.4020 0.1527 47 2.633
## near: Session 1 last block vs washout block 2 -0.0576 0.0788 47 -0.731
## Near: washout block 1 vs washout block 2 -0.4595 0.1292 47 -3.558
## p.value
## 1.0000
## 1.0000
## 0.1363
## <.0001
## 1.0000
## <.0001
## 0.1028
## 1.0000
## 0.0078
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 Far: Session 1 last block vs washout block 1 0.05214180
## 2 Far: Session 1 last block vs washout block 2 0.01297803
## 3 Far: washout block 1 vs washout block 2 0.11913683
## 4 Mid: Session 1 last block vs washout block 1 0.42599124
## 5 Mid: Session 1 last block vs washout block 2 0.01311947
## 6 Mid: washout block 1 vs washout block 2 0.45082245
## 7 Near: Session 1 last block vs washout block 1 0.12853985
## 8 near: Session 1 last block vs washout block 2 0.01122912
## 9 Near: washout block 1 vs washout block 2 0.21216958RAEUntrainedHandMTComparisonsBayesfollowup()## Bayesian t-test Far: Session 1 last block vs Washout Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5187171 ±0.03%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Session 1 last block vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.20989 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Washout block 1 vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.67669 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 last block vs Washout Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 41540.7 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 last block vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2105628 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Washout block 1 vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 113088.6 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 last block vs Washout Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.404626 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 last block vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2017538 ±0.06%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Washout block 1 vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 32.78584 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSOverall, we find differences from the first block of washout, especially for the middle target.
Path length
We compare path length during the first two blocks of session 2 washout with those during the last block of aligned reaches using the nondominant hand in session 1. We conduct a 3x3 (target x block) within-subjects ANOVA.
RAEUntrainedHandPLANOVA()## Comparing path length during washout trials with aligned trials across targets and blocks, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 5.561672 5.213724e-03 * 0.02457008
## 3 block 2 94 37.716285 9.422258e-13 * 0.14607978
## 4 target:block 4 188 4.721751 1.183981e-03 * 0.03741688
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.83166098 1.441337e-02 *
## 3 block 0.31667886 3.267674e-12 *
## 4 target:block 0.05933572 3.112965e-23 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.8559160 7.940270e-03 * 0.8850869 7.290767e-03
## 3 block 0.5940637 1.680791e-08 * 0.6006098 1.434437e-08
## 4 target:block 0.5277673 9.796014e-03 * 0.5532061 8.726524e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *RAEUntrainedHandPLBayesANOVA()## Comparing path length during washout trials with aligned trials across targets and blocks, untrained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 2.419877 ±1.77%
## [2] block + participant : 1.062616e+13 ±0.89%
## [3] target + block + participant : 5.67356e+13 ±1.38%
## [4] target + block + target:block + participant : 1.110834e+15 ±5.72%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.99 73.25
## block 0.60 1.00 2.30e+14
## block:target 0.20 0.94 65.96
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find target x block interaction
RAEUntrainedHandPLComparisonMeans()## target block emmean SE df lower.CL upper.CL
## far s1_last 0.477 0.00850 47 0.460 0.494
## mid s1_last 0.475 0.01039 47 0.454 0.496
## near s1_last 0.501 0.01747 47 0.465 0.536
## far first 0.637 0.04140 47 0.554 0.720
## mid first 0.797 0.06537 47 0.666 0.929
## near first 0.583 0.04057 47 0.502 0.665
## far second 0.474 0.01560 47 0.443 0.505
## mid second 0.513 0.01739 47 0.478 0.548
## near second 0.471 0.00912 47 0.452 0.489
##
## Confidence level used: 0.95RAEUntrainedHandPLComparisonsEffSize()## contrast estimate SE df t.ratio
## Far: Session 1 last block vs washout block 1 0.1601 0.0390 47 4.103
## Far: Session 1 last block vs washout block 2 -0.0026 0.0185 47 -0.140
## Far: washout block 1 vs washout block 2 -0.1627 0.0453 47 -3.588
## Mid: Session 1 last block vs washout block 1 0.3225 0.0655 47 4.923
## Mid: Session 1 last block vs washout block 2 0.0380 0.0174 47 2.189
## Mid: washout block 1 vs washout block 2 -0.2845 0.0581 47 -4.893
## Near: Session 1 last block vs washout block 1 0.0827 0.0439 47 1.885
## near: Session 1 last block vs washout block 2 -0.0299 0.0189 47 -1.576
## Near: washout block 1 vs washout block 2 -0.1126 0.0396 47 -2.843
## p.value
## 0.0014
## 1.0000
## 0.0071
## 0.0001
## 0.3027
## 0.0001
## 0.5908
## 1.0000
## 0.0593
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 Far: Session 1 last block vs washout block 1 0.2636885260
## 2 Far: Session 1 last block vs washout block 2 0.0004170336
## 3 Far: washout block 1 vs washout block 2 0.2150358984
## 4 Mid: Session 1 last block vs washout block 1 0.3402630573
## 5 Mid: Session 1 last block vs washout block 2 0.0924857591
## 6 Mid: washout block 1 vs washout block 2 0.3374837440
## 7 Near: Session 1 last block vs washout block 1 0.0702725032
## 8 near: Session 1 last block vs washout block 2 0.0501944838
## 9 Near: washout block 1 vs washout block 2 0.1467700312RAEUntrainedHandPLComparisonsBayesfollowup()## Bayesian t-test Far: Session 1 last block vs Washout Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 150.1486 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Session 1 last block vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1582578 ±0.07%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Far: Washout block 1 vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 35.58547 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 last block vs Washout Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1785.744 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Session 1 last block vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.372832 ±0.02%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Mid: Washout block 1 vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1624.071 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 last block vs Washout Block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7990002 ±0.03%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Session 1 last block vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4954505 ±0.04%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
##
## Bayesian t-test Near: Washout block 1 vs Washout Block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5.469646 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests show that the interaction is driven by the longer path lengths for the middle and far targets during the first block of washout compared to the first block of aligned reaches and second block of washout.
Study 2: Supplementary analyses for the online experiment
Given the large sample we were able to collect for the online study, we also investigate for any effects related to the device they used to control the cursor (either a mouse or trackpad), and for any effects related to the participants’ sex. Therefore, we split the data into mouse and trackpad users, and into males and females.
Session 1
Device used: Mouse vs. trackpad
Learning
plotDeviceCtrl()
We first plot angular reach deviations across trial types for each of the target locations. We observe large variability for the mouse users due to their sample being disproportionately lower than trackpad users (Mouse N = 19, Trackpad N = 44). However, we do not really see much of a difference in learning rates and asymptotes.
First, we test for an effect of device used in the two sets of aligned trials where participants either used their dominant or nondominant hand. We conduct a 3x3x2 mixed design ANOVA, with target and block as within-subjects factors and device as a between-subjects factor.
deviceAlignedLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during aligned trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 3.0286463 0.08684903 0.005131584
## 3 block 2 122 0.3352930 0.71578539 0.001225883
## 5 target 2 122 3.5081228 0.03300968 * 0.013232738
## 4 devices:block 2 122 1.3520011 0.26257040 0.004924819
## 6 devices:target 2 122 0.3527732 0.70345100 0.001346699
## 7 block:target 4 244 1.0506891 0.38167776 0.007515510
## 8 devices:block:target 4 244 2.0164606 0.09276629 0.014324655
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9895788 0.7303180
## 4 devices:block 0.9895788 0.7303180
## 5 target 0.9537018 0.2412003
## 6 devices:target 0.9537018 0.2412003
## 7 block:target 0.8399753 0.3222309
## 8 devices:block:target 0.8399753 0.3222309
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9896863 0.71356152 1.0227026 0.71578539
## 4 devices:block 0.9896863 0.26254923 1.0227026 0.26257040
## 5 target 0.9557505 0.03511767 * 0.9859199 0.03366625
## 6 devices:target 0.9557505 0.69382427 0.9859199 0.70043877
## 7 block:target 0.9222250 0.37904686 0.9889524 0.38132794
## 8 devices:block:target 0.9222250 0.09868474 0.9889524 0.09358392
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during aligned trials across targets, blocks, and devices, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.5155845 0.4754725 0.001285841
## 3 block 2 122 1.0882920 0.3400380 0.003317962
## 5 target 2 122 1.2473436 0.2909040 0.005089616
## 4 devices:block 2 122 0.3646288 0.6952086 0.001114131
## 6 devices:target 2 122 1.2705923 0.2843526 0.005183987
## 7 block:target 4 244 0.6116591 0.6546188 0.004103301
## 8 devices:block:target 4 244 1.8741660 0.1155651 0.012467209
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9137101 0.0667194277
## 4 devices:block 0.9137101 0.0667194277
## 5 target 0.9955014 0.8734854864
## 6 devices:target 0.9955014 0.8734854864
## 7 block:target 0.5829693 0.0001954457 *
## 8 devices:block:target 0.5829693 0.0001954457 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9205645 0.3362114 0.9478714 0.3375897
## 4 devices:block 0.9205645 0.6777227 0.9478714 0.6839087
## 5 target 0.9955215 0.2908269 1.0290359 0.2909040
## 6 devices:target 0.9955215 0.2842915 1.0290359 0.2843526
## 7 block:target 0.8050210 0.6195958 0.8551639 0.6293120
## 8 devices:block:target 0.8050210 0.1308638 0.8551639 0.1267539
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8deviceAlignedLearningBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 2.395291 ±0.61%
## [2] block + participant : 0.0230861 ±1.14%
## [3] target + block + participant : 0.05362267 ±0.86%
## [4] target + block + target:block + participant : 0.0107758 ±1.81%
## [5] devices + participant : 0.283943 ±1.05%
## [6] target + devices + participant : 0.6932279 ±1.6%
## [7] block + devices + participant : 0.006498914 ±1.31%
## [8] target + block + devices + participant : 0.01592288 ±2.16%
## [9] target + block + target:block + devices + participant : 0.003030676 ±1.6%
## [10] target + devices + target:devices + participant : 0.04453235 ±2.63%
## [11] target + block + devices + target:devices + participant : 0.001000688 ±1.8%
## [12] target + block + target:block + devices + target:devices + participant : 0.0001992936 ±2.11%
## [13] block + devices + block:devices + participant : 0.001012052 ±3.21%
## [14] target + block + devices + block:devices + participant : 0.002649613 ±7.51%
## [15] target + block + target:block + devices + block:devices + participant : 0.0005451429 ±12.23%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0001455547 ±2.01%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3.449765e-05 ±4.87%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 2.23382e-05 ±11.94%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.71 0.875
## block 0.74 0.03 0.010
## block:target 0.32 3.22e-03 0.007
## devices 0.74 0.23 0.108
## devices:target 0.32 0.01 0.022
## block:devices 0.32 9.72e-04 0.002
## block:devices:target 0.05 4.93e-06 8.87e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04136545 ±0.94%
## [2] block + participant : 0.07361394 ±1.03%
## [3] target + block + participant : 0.003077835 ±1.38%
## [4] target + block + target:block + participant : 0.0001002301 ±6.9%
## [5] devices + participant : 0.1657431 ±0.95%
## [6] target + devices + participant : 0.007727847 ±6.78%
## [7] block + devices + participant : 0.01225059 ±1.8%
## [8] target + block + devices + participant : 0.0005125919 ±1.91%
## [9] target + block + target:block + devices + participant : 1.662885e-05 ±6.48%
## [10] target + devices + target:devices + participant : 0.001131886 ±1.56%
## [11] target + block + devices + target:devices + participant : 8.126331e-05 ±1.55%
## [12] target + block + target:block + devices + target:devices + participant : 2.721035e-06 ±2.22%
## [13] block + devices + block:devices + participant : 0.0007164452 ±1.97%
## [14] target + block + devices + block:devices + participant : 3.775885e-05 ±16.46%
## [15] target + block + target:block + devices + block:devices + participant : 1.372419e-06 ±26.19%
## [16] target + block + devices + target:devices + block:devices + participant : 4.795573e-06 ±1.8%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.715989e-07 ±7.3%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 6.531829e-08 ±3.69%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.04 0.015
## block 0.74 0.07 0.027
## block:target 0.32 9.28e-05 2.01e-04
## devices 0.74 0.14 0.060
## devices:target 0.32 9.35e-04 0.002
## block:devices 0.32 5.82e-04 0.001
## block:devices:target 0.05 5.00e-08 9.00e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no effects related to device used, suggestting that aligned reaches for both hands did not differ between mouse or trackpad users.
We then conducted the same 3x3x2 mixed design ANOVA during the mirror reversed trials.
devicemirrorANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 1.1566617 0.2863944 0.0018473042
## 3 target 2 122 1.7540801 0.1774026 0.0052519560
## 5 block 2 122 0.1222263 0.8850563 0.0004710773
## 4 devices:target 2 122 0.5014826 0.6068750 0.0015071600
## 6 devices:block 2 122 0.3151887 0.7302436 0.0012138787
## 7 target:block 4 244 0.3842324 0.8198233 0.0030367463
## 8 devices:target:block 4 244 0.1983549 0.9390675 0.0015699870
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.079907839 1.195863e-33 *
## 4 devices:target 0.079907839 1.195863e-33 *
## 5 block 0.781192494 6.063758e-04 *
## 6 devices:block 0.781192494 6.063758e-04 *
## 7 target:block 0.001261774 1.368065e-79 *
## 8 devices:target:block 0.001261774 1.368065e-79 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.5208083 0.1902924 0.5218639 0.1902894
## 4 devices:target 0.5208083 0.4887667 0.5218639 0.4891259
## 5 block 0.8204741 0.8456783 0.8401313 0.8506704
## 6 devices:block 0.8204741 0.6869185 0.8401313 0.6921489
## 7 target:block 0.4202281 0.6455762 0.4307912 0.6507600
## 8 devices:target:block 0.4202281 0.7821787 0.4307912 0.7877780
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8devicemirrorBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.2381704 ±1.16%
## [2] block + participant : 0.02938461 ±0.67%
## [3] target + block + participant : 0.007251742 ±3.85%
## [4] target + block + target:block + participant : 0.0002078653 ±1.5%
## [5] devices + participant : 0.1785455 ±2.69%
## [6] target + devices + participant : 0.04048402 ±1.02%
## [7] block + devices + participant : 0.005075873 ±1.2%
## [8] target + block + devices + participant : 0.001266977 ±3.07%
## [9] target + block + target:block + devices + participant : 3.587813e-05 ±1.73%
## [10] target + devices + target:devices + participant : 0.002836174 ±2.2%
## [11] target + block + devices + target:devices + participant : 8.331294e-05 ±2.13%
## [12] target + block + target:block + devices + target:devices + participant : 2.472036e-06 ±2.36%
## [13] block + devices + block:devices + participant : 0.0003117311 ±2.67%
## [14] target + block + devices + block:devices + participant : 7.845945e-05 ±4.07%
## [15] target + block + target:block + devices + block:devices + participant : 2.203034e-06 ±2.45%
## [16] target + block + devices + target:devices + block:devices + participant : 4.890326e-06 ±2.33%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.593695e-07 ±7.38%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 5.562053e-09 ±2.49%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.19 0.085
## block 0.74 0.03 0.011
## block:target 0.32 1.65e-04 3.58e-04
## devices 0.74 0.15 0.064
## devices:target 0.32 1.95e-03 0.004
## block:devices 0.32 2.64e-04 5.73e-04
## block:devices:target 0.05 3.70e-09 6.66e-08
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects related to device used. Finally, we run the same 3x3x2 mixed design ANOVA for the washout trials.
RAEDeviceLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during washout trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.63242864 0.4295495 1.764595e-03
## 3 block 1 61 0.57125565 0.4526692 1.464511e-03
## 5 target 2 122 0.10535655 0.9000854 6.532352e-04
## 4 devices:block 1 61 0.01621664 0.8990865 4.163337e-05
## 6 devices:target 2 122 0.31472898 0.7305776 1.948863e-03
## 7 block:target 2 122 0.17282975 0.8414864 8.334856e-04
## 8 devices:block:target 2 122 0.57698215 0.5631155 2.777131e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9500933 0.2152722
## 6 devices:target 0.9500933 0.2152722
## 7 block:target 0.9799965 0.5454258
## 8 devices:block:target 0.9799965 0.5454258
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 5 target 0.9524656 0.8914056 0.982364 0.8969583
## 6 devices:target 0.9524656 0.7200054 0.982364 0.7267233
## 7 block:target 0.9803888 0.8373849 1.012617 0.8414864
## 8 devices:block:target 0.9803888 0.5598406 1.012617 0.5631155
## p[HF]<.05
## 5
## 6
## 7
## 8RAEDeviceLearningBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.02924976 ±0.78%
## [2] block + participant : 0.1510585 ±1.37%
## [3] target + block + participant : 0.004382482 ±1.12%
## [4] target + block + target:block + participant : 0.0003880924 ±1.67%
## [5] devices + participant : 0.188525 ±1.18%
## [6] target + devices + participant : 0.005699896 ±1.66%
## [7] block + devices + participant : 0.02949938 ±3.31%
## [8] target + block + devices + participant : 0.0009248429 ±8.96%
## [9] target + block + target:block + devices + participant : 7.951282e-05 ±4.68%
## [10] target + devices + target:devices + participant : 0.0004871741 ±4.84%
## [11] target + block + devices + target:devices + participant : 8.665916e-05 ±12.8%
## [12] target + block + target:block + devices + target:devices + participant : 6.156622e-06 ±2.28%
## [13] block + devices + block:devices + participant : 0.004726844 ±2.43%
## [14] target + block + devices + block:devices + participant : 0.000139609 ±4%
## [15] target + block + target:block + devices + block:devices + participant : 1.301497e-05 ±5.03%
## [16] target + block + devices + target:devices + block:devices + participant : 1.361904e-05 ±5.67%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.107019e-06 ±4%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1.797389e-07 ±5.55%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.011
## block 0.74 0.14 0.056
## block:target 0.32 3.45e-04 7.47e-04
## devices 0.74 0.16 0.069
## devices:target 0.32 4.20e-04 9.11e-04
## block:devices 0.32 3.46e-03 0.008
## block:devices:target 0.05 1.27e-07 2.29e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no effects related to device used. Taken together, our results suggest that using either a mouse or trackpad to control the cursor does not lead to any differences in learning to compensate for the mirror reversed perturbation.
Completion time
Next, we looked into completion time between the two devices.
plotDeviceCtrlMT()
We conduct the same 3x3x2 (target x block x device) mixed design ANOVA as in learning, but we now have completion time as the dependent variable.
deviceAlignedMTANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during aligned trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 1.3613313 0.2478479926 0.0182710204
## 3 block 2 122 9.1606857 0.0001965154 * 0.0123585242
## 5 target 2 122 2.4112045 0.0939709859 0.0025917845
## 4 devices:block 2 122 1.2416629 0.2925280532 0.0016931953
## 6 devices:target 2 122 0.5162488 0.5980526507 0.0005560443
## 7 block:target 4 244 0.8528533 0.4929931685 0.0002375235
## 8 devices:block:target 4 244 1.2005976 0.3111549135 0.0003343394
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.3101534 5.588532e-16 *
## 4 devices:block 0.3101534 5.588532e-16 *
## 5 target 0.2883291 6.261160e-17 *
## 6 devices:target 0.2883291 6.261160e-17 *
## 7 block:target 0.6035022 4.401207e-04 *
## 8 devices:block:target 0.6035022 4.401207e-04 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.5917697 0.002112457 * 0.5966539 0.002052872
## 4 devices:block 0.5917697 0.276975803 0.5966539 0.277310417
## 5 target 0.5842245 0.120418552 0.5886847 0.120132311
## 6 devices:target 0.5842245 0.502333633 0.5886847 0.503667600
## 7 block:target 0.8081101 0.473573200 0.8586623 0.479121721
## 8 devices:block:target 0.8081101 0.311371210 0.8586623 0.311513749
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during aligned trials across targets, blocks, and devices, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.52280456 0.47241117 0.0059037276
## 3 block 2 122 3.66806859 0.02838158 * 0.0099897617
## 5 target 2 122 1.50936145 0.22514957 0.0012439513
## 4 devices:block 2 122 1.08348472 0.34164786 0.0029717226
## 6 devices:target 2 122 0.48565360 0.61647930 0.0004005930
## 7 block:target 4 244 0.08789517 0.98615829 0.0001281222
## 8 devices:block:target 4 244 0.49388918 0.74023879 0.0007195019
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.4419950 2.304207e-11 *
## 4 devices:block 0.4419950 2.304207e-11 *
## 5 target 0.9834748 6.065923e-01
## 6 devices:target 0.9834748 6.065923e-01
## 7 block:target 0.2681920 3.818763e-13 *
## 8 devices:block:target 0.2681920 3.818763e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6418465 0.0487957 * 0.6496464 0.04822887
## 4 devices:block 0.6418465 0.3180755 0.6496464 0.31880306
## 5 target 0.9837434 0.2254235 1.0162551 0.22514957
## 6 devices:target 0.9837434 0.6134069 1.0162551 0.61647930
## 7 block:target 0.5856198 0.9391284 0.6104660 0.94449326
## 8 devices:block:target 0.5856198 0.6408572 0.6104660 0.64859814
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8deviceAlignedMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 3.321393 ±4.14%
## [2] block + participant : 2077253093 ±0.96%
## [3] target + block + participant : 12903724120 ±7.57%
## [4] target + block + target:block + participant : 96619331 ±1.51%
## [5] devices + participant : 0.6742244 ±1.33%
## [6] target + devices + participant : 2.099726 ±1.34%
## [7] block + devices + participant : 1433313176 ±1.73%
## [8] target + block + devices + participant : 7903383627 ±1.8%
## [9] target + block + target:block + devices + participant : 68062479 ±2.82%
## [10] target + devices + target:devices + participant : 0.19388 ±2.11%
## [11] target + block + devices + target:devices + participant : 794942596 ±3.99%
## [12] target + block + target:block + devices + target:devices + participant : 6911186 ±5.24%
## [13] block + devices + block:devices + participant : 856647243 ±17.16%
## [14] target + block + devices + block:devices + participant : 4028213136 ±4.35%
## [15] target + block + target:block + devices + block:devices + participant : 33056531 ±2.06%
## [16] target + block + devices + target:devices + block:devices + participant : 446459644 ±8.21%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3120307 ±2.88%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 107885.2 ±3.04%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.86 2.15
## block 0.74 1.00 1.50e+09
## block:target 0.32 6.78e-03 0.015
## devices 0.74 0.51 0.369
## devices:target 0.32 0.04 0.092
## block:devices 0.32 0.18 0.460
## block:devices:target 0.05 3.52e-06 6.34e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.07805056 ±0.89%
## [2] block + participant : 7288.692 ±0.67%
## [3] target + block + participant : 615.1048 ±1.95%
## [4] target + block + target:block + participant : 5.775828 ±1.16%
## [5] devices + participant : 0.4375002 ±0.8%
## [6] target + devices + participant : 0.03351447 ±1.35%
## [7] block + devices + participant : 3226.788 ±1.49%
## [8] target + block + devices + participant : 299.352 ±12.12%
## [9] target + block + target:block + devices + participant : 2.582626 ±1.96%
## [10] target + devices + target:devices + participant : 0.002000206 ±3.79%
## [11] target + block + devices + target:devices + participant : 16.17596 ±2.86%
## [12] target + block + target:block + devices + target:devices + participant : 0.1619393 ±4.3%
## [13] block + devices + block:devices + participant : 1384.48 ±1.89%
## [14] target + block + devices + block:devices + participant : 116.4607 ±2.08%
## [15] target + block + target:block + devices + block:devices + participant : 1.107888 ±2.4%
## [16] target + block + devices + target:devices + block:devices + participant : 8.126758 ±13.38%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.07010441 ±5.34%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.002517318 ±2.85%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.08 0.032
## block 0.74 1.00 2.99e+03
## block:target 0.32 7.48e-04 0.002
## devices 0.74 0.39 0.228
## devices:target 0.32 1.89e-03 0.004
## block:devices 0.32 0.12 0.286
## block:devices:target 0.05 1.94e-07 3.49e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects. We repeat the test for the mirror reversed trials.
deviceMirrorMTANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 2.36353429 1.293718e-01 1.084670e-02
## 3 target 2 122 19.82819934 3.497702e-08 * 5.922950e-02
## 5 block 2 122 31.44561522 9.683996e-12 * 1.037904e-01
## 4 devices:target 2 122 0.00642518 9.935958e-01 2.040081e-05
## 6 devices:block 2 122 1.43145493 2.429456e-01 5.244229e-03
## 7 target:block 4 244 3.43595657 9.374931e-03 * 1.654364e-02
## 8 devices:target:block 4 244 0.11076984 9.786752e-01 5.420190e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9744371 4.598487e-01
## 4 devices:target 0.9744371 4.598487e-01
## 5 block 0.6681273 5.568999e-06 *
## 6 devices:block 0.6681273 5.568999e-06 *
## 7 target:block 0.2711276 5.126848e-13 *
## 8 devices:target:block 0.2711276 5.126848e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.9750743 4.937779e-08 * 1.0068545 3.497702e-08
## 4 devices:target 0.9750743 9.928407e-01 1.0068545 9.935958e-01
## 5 block 0.7508225 2.189013e-09 * 0.7655841 1.586700e-09
## 6 devices:block 0.7508225 2.431447e-01 0.7655841 2.432691e-01
## 7 target:block 0.5713525 2.917151e-02 * 0.5948071 2.739186e-02
## 8 devices:target:block 0.5713525 9.175299e-01 0.5948071 9.236751e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8deviceMirrorMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 7832344 ±1.18%
## [2] block + participant : 5.098732e+16 ±1.45%
## [3] target + block + participant : 1.79151e+25 ±2.73%
## [4] target + block + target:block + participant : 2.207661e+25 ±1.07%
## [5] devices + participant : 0.4354577 ±1.36%
## [6] target + devices + participant : 3418809 ±1.27%
## [7] block + devices + participant : 2.466569e+16 ±4.08%
## [8] target + block + devices + participant : 8.21173e+24 ±1.92%
## [9] target + block + target:block + devices + participant : 1.169935e+25 ±3.49%
## [10] target + devices + target:devices + participant : 150581.4 ±1.29%
## [11] target + block + devices + target:devices + participant : 4.063437e+23 ±8.84%
## [12] target + block + target:block + devices + target:devices + participant : 4.931823e+23 ±2.23%
## [13] block + devices + block:devices + participant : 4.913834e+15 ±1.99%
## [14] target + block + devices + block:devices + participant : 2.145496e+24 ±3.57%
## [15] target + block + target:block + devices + block:devices + participant : 2.744993e+24 ±2.11%
## [16] target + block + devices + target:devices + block:devices + participant : 8.683079e+22 ±2.2%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.248889e+23 ±2.96%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 3.380692e+21 ±2.45%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.92e+08
## block 0.74 1.00 2.06e+18
## block:target 0.32 0.56 2.80
## devices 0.74 0.39 0.231
## devices:target 0.32 0.02 0.037
## block:devices 0.32 0.08 0.182
## block:devices:target 0.05 5.13e-05 9.23e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects. Finally, we conduct the test for washout trials.
deviceRAEMTANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during washout trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 2.1349369 1.491086e-01 0.0263468832
## 3 block 1 61 33.1891541 2.935277e-07 * 0.0158326605
## 5 target 2 122 4.6816600 1.099078e-02 * 0.0078773785
## 4 devices:block 1 61 4.7946598 3.238280e-02 * 0.0023186672
## 6 devices:target 2 122 0.9814930 3.776904e-01 0.0016618101
## 7 block:target 2 122 0.1618102 8.507848e-01 0.0002488015
## 8 devices:block:target 2 122 0.4615610 6.313951e-01 0.0007093751
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9984388 0.9542090
## 6 devices:target 0.9984388 0.9542090
## 7 block:target 0.9391364 0.1520056
## 8 devices:block:target 0.9391364 0.1520056
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 5 target 0.9984412 0.01102987 * 1.0322057 0.01099078
## 6 devices:target 0.9984412 0.37758658 1.0322057 0.37769036
## 7 block:target 0.9426282 0.83861482 0.9717195 0.84492612
## 8 devices:block:target 0.9426282 0.62000645 0.9717195 0.62586396
## p[HF]<.05
## 5 *
## 6
## 7
## 8deviceRAEMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1.699309 ±6.89%
## [2] block + participant : 507660.8 ±2.5%
## [3] target + block + participant : 1166724 ±1.19%
## [4] target + block + target:block + participant : 69825.98 ±2.06%
## [5] devices + participant : 0.816394 ±2%
## [6] target + devices + participant : 1.320844 ±2.8%
## [7] block + devices + participant : 426848.6 ±2.56%
## [8] target + block + devices + participant : 991725.8 ±3.6%
## [9] target + block + target:block + devices + participant : 58007.58 ±2.06%
## [10] target + devices + target:devices + participant : 0.1664361 ±1.53%
## [11] target + block + devices + target:devices + participant : 146674.6 ±2.88%
## [12] target + block + target:block + devices + target:devices + participant : 8961.926 ±10.27%
## [13] block + devices + block:devices + participant : 298742.1 ±2.03%
## [14] target + block + devices + block:devices + participant : 764195.9 ±2.42%
## [15] target + block + target:block + devices + block:devices + participant : 47221.77 ±4%
## [16] target + block + devices + target:devices + block:devices + participant : 121499.9 ±8.75%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 8148.576 ±11.5%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1100.293 ±7.69%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.73 0.980
## block 0.74 1.00 3.30e+05
## block:target 0.32 0.04 0.095
## devices 0.74 0.62 0.588
## devices:target 0.32 0.06 0.143
## block:devices 0.32 0.27 0.796
## block:devices:target 0.05 2.38e-04 0.004
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a device x block interaction in the frequentist test, which did not hold up in the Bayesian test. Overall, completion time did not differ between mouse and trackpad users.
Path length
We also looked into path lengths for the two devices.
plotDeviceCtrlPL()
We then repeat the same set of ANOVAs as in the section above, but use path length as the dependent variable. We first look into the aligned trials.
deviceAlignedPLANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during aligned trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.5504171 0.4609944122 0.0046867046
## 3 block 2 122 1.8857279 0.1561141707 0.0046772311
## 5 target 2 122 7.7126879 0.0007012401 * 0.0165534340
## 4 devices:block 2 122 2.4134929 0.0937643504 0.0059784376
## 6 devices:target 2 122 0.2493412 0.7797101483 0.0005438629
## 7 block:target 4 244 0.2184723 0.9279933240 0.0006908018
## 8 devices:block:target 4 244 0.9668977 0.4262749757 0.0030500783
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8091827 0.001743401 *
## 4 devices:block 0.8091827 0.001743401 *
## 5 target 0.9719612 0.426057099
## 6 devices:target 0.9719612 0.426057099
## 7 block:target 0.7121979 0.016956811 *
## 8 devices:block:target 0.7121979 0.016956811 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8397594 0.1633126096 0.8608339 0.1623910536
## 4 devices:block 0.8397594 0.1036110593 0.8608339 0.1022764312
## 5 target 0.9727259 0.0007958683 * 1.0043089 0.0007012401
## 6 devices:target 0.9727259 0.7736631185 1.0043089 0.7797101483
## 7 block:target 0.8653131 0.9070130252 0.9237151 0.9168466151
## 8 devices:block:target 0.8653131 0.4180711098 0.9237151 0.4218219495
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during aligned trials across targets, blocks, and devices, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 8.840270 0.0042146884 * 0.041076047
## 3 block 2 122 8.196806 0.0004569524 * 0.021254677
## 5 target 2 122 3.189158 0.0446640054 * 0.009075748
## 4 devices:block 2 122 3.492965 0.0334862964 * 0.009169250
## 6 devices:target 2 122 5.422812 0.0055432854 * 0.015334835
## 7 block:target 4 244 1.830192 0.1236138273 0.010909692
## 8 devices:block:target 4 244 2.947909 0.0209193088 * 0.017456054
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9176398 0.075886975
## 4 devices:block 0.9176398 0.075886975
## 5 target 0.8828178 0.023775616 *
## 6 devices:target 0.8828178 0.023775616 *
## 7 block:target 0.6347790 0.001403033 *
## 8 devices:block:target 0.6347790 0.001403033 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9239068 0.0006698352 * 0.9514817 0.0005830777
## 4 devices:block 0.9239068 0.0372164464 * 0.9514817 0.0358188578
## 5 target 0.8951091 0.0504807632 0.9204014 0.0490134867
## 6 devices:target 0.8951091 0.0074769310 * 0.9204014 0.0069557507
## 7 block:target 0.8090715 0.1383563219 0.8597513 0.1342915754
## 8 devices:block:target 0.8090715 0.0304052879 * 0.8597513 0.0275191056
## p[HF]<.05
## 3 *
## 4 *
## 5 *
## 6 *
## 7
## 8 *deviceAlignedPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 209.16 ±1.47%
## [2] block + participant : 0.04602667 ±0.95%
## [3] target + block + participant : 9.838867 ±3.37%
## [4] target + block + target:block + participant : 0.07300303 ±1.29%
## [5] devices + participant : 0.3340053 ±0.59%
## [6] target + devices + participant : 69.73161 ±1.37%
## [7] block + devices + participant : 0.01585573 ±2.64%
## [8] target + block + devices + participant : 3.411918 ±2.17%
## [9] target + block + target:block + devices + participant : 0.02487539 ±1.47%
## [10] target + devices + target:devices + participant : 3.775619 ±1.4%
## [11] target + block + devices + target:devices + participant : 0.1843105 ±2.71%
## [12] target + block + target:block + devices + target:devices + participant : 0.001479221 ±6.27%
## [13] block + devices + block:devices + participant : 0.008937829 ±1.34%
## [14] target + block + devices + block:devices + participant : 2.124812 ±1.91%
## [15] target + block + target:block + devices + block:devices + participant : 0.01611336 ±2.08%
## [16] target + block + devices + target:devices + block:devices + participant : 0.1895017 ±35.36%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.0008943175 ±2.96%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 6.416131e-05 ±2.78%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 75.89
## block 0.74 0.05 0.020
## block:target 0.32 3.88e-04 8.41e-04
## devices 0.74 0.27 0.130
## devices:target 0.32 0.01 0.030
## block:devices 0.32 7.80e-03 0.017
## block:devices:target 0.05 2.14e-07 3.85e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04425777 ±1.27%
## [2] block + participant : 2.659766 ±1.39%
## [3] target + block + participant : 0.12063 ±2.38%
## [4] target + block + target:block + participant : 0.003724124 ±2.73%
## [5] devices + participant : 6.86808 ±1.05%
## [6] target + devices + participant : 0.2955271 ±1.24%
## [7] block + devices + participant : 18.25934 ±1.32%
## [8] target + block + devices + participant : 0.8189561 ±1.95%
## [9] target + block + target:block + devices + participant : 0.02773897 ±6.09%
## [10] target + devices + target:devices + participant : 1.337763 ±9.56%
## [11] target + block + devices + target:devices + participant : 3.874747 ±5.07%
## [12] target + block + target:block + devices + target:devices + participant : 0.1553856 ±25.93%
## [13] block + devices + block:devices + participant : 11.27252 ±1.49%
## [14] target + block + devices + block:devices + participant : 0.5000238 ±1.78%
## [15] target + block + target:block + devices + block:devices + participant : 0.01752691 ±5.89%
## [16] target + block + devices + target:devices + block:devices + participant : 2.260415 ±1.78%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.08134232 ±4.17%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.1380346 ±2.46%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.19 0.086
## block 0.74 0.81 1.50
## block:target 0.32 8.52e-03 0.019
## devices 0.74 0.92 4.28
## devices:target 0.32 0.16 0.406
## block:devices 0.32 0.29 0.872
## block:devices:target 0.05 2.78e-03 0.050
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects for the dominant hand, but find a main effect of device and a target x block x device interaction for the nondominant hand. We conduct follow-up tests on the main effect of device, regardless of target or block.
deviceAlignedPLComparisons()##
## Welch Two Sample t-test
##
## data: mousedat$pathlength and trackdat$pathlength
## t = 2.7565, df = 29.151, p-value = 0.009974
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.01569437 0.10587877
## sample estimates:
## mean of x mean of y
## 0.5491369 0.4883503
##
## Bayesian t-test (mouse vs. trackpad):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 9.43347 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe find longer path lengths for mouse users, than trackpad users.
Next, we test for effects in the mirror reversed trials.
deviceMirrorPLANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.1568998 6.934091e-01 0.0004802307
## 3 target 2 122 19.8162205 3.529468e-08 * 0.0615998597
## 5 block 2 122 23.6154692 2.141333e-09 * 0.0993070369
## 4 devices:target 2 122 0.8487445 4.304629e-01 0.0028036802
## 6 devices:block 2 122 0.2824242 7.544454e-01 0.0013168500
## 7 target:block 4 244 4.1297597 2.954244e-03 * 0.0216158047
## 8 devices:target:block 4 244 1.0035359 4.063112e-01 0.0053400430
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9996237 9.887710e-01
## 4 devices:target 0.9996237 9.887710e-01
## 5 block 0.4608833 8.085902e-11 *
## 6 devices:block 0.4608833 8.085902e-11 *
## 7 target:block 0.1833458 1.151926e-17 *
## 8 devices:target:block 0.1833458 1.151926e-17 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.9996238 3.547868e-08 * 1.033490 3.529468e-08
## 4 devices:target 0.9996238 4.304265e-01 1.033490 4.304629e-01
## 5 block 0.6497233 7.077443e-07 * 0.657998 6.167683e-07
## 6 devices:block 0.6497233 6.573445e-01 0.657998 6.602508e-01
## 7 target:block 0.6474644 1.065412e-02 * 0.678697 9.497773e-03
## 8 devices:target:block 0.6474644 3.846891e-01 0.678697 3.872558e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8deviceMirrorPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1626100 ±0.95%
## [2] block + participant : 6.822977e+13 ±0.81%
## [3] target + block + participant : 1.712959e+21 ±0.93%
## [4] target + block + target:block + participant : 8.63282e+21 ±1.5%
## [5] devices + participant : 0.1469406 ±0.94%
## [6] target + devices + participant : 239546.8 ±1.27%
## [7] block + devices + participant : 1.015636e+13 ±1.11%
## [8] target + block + devices + participant : 2.732004e+20 ±1.48%
## [9] target + block + target:block + devices + participant : 1.374455e+21 ±2.14%
## [10] target + devices + target:devices + participant : 20703.5 ±4.39%
## [11] target + block + devices + target:devices + participant : 2.557316e+19 ±2.53%
## [12] target + block + target:block + devices + target:devices + participant : 1.23814e+20 ±2.32%
## [13] block + devices + block:devices + participant : 6.86888e+11 ±3.47%
## [14] target + block + devices + block:devices + participant : 1.909526e+19 ±5.69%
## [15] target + block + target:block + devices + block:devices + participant : 9.417696e+19 ±4.39%
## [16] target + block + devices + target:devices + block:devices + participant : 1.632307e+18 ±2.37%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 9.210817e+18 ±4.89%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 6.786852e+17 ±2.37%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.54e+07
## block 0.74 1.00 2.32e+15
## block:target 0.32 0.83 10.91
## devices 0.74 0.16 0.066
## devices:target 0.32 0.01 0.029
## block:devices 0.32 0.01 0.022
## block:devices:target 0.05 5.53e-05 9.96e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects. We then test for an effect during washout trials.
deviceRAEPLANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during washout trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.48478101 0.4889093 0.0029353455
## 3 block 1 61 6.02978819 0.0169312 * 0.0143750276
## 5 target 2 122 0.02424711 0.9760492 0.0001111229
## 4 devices:block 1 61 0.06538257 0.7990426 0.0001581205
## 6 devices:target 2 122 2.02521820 0.1363779 0.0091970993
## 7 block:target 2 122 0.94176174 0.3927563 0.0031154151
## 8 devices:block:target 2 122 1.21519218 0.3002180 0.0040163096
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9204901 0.08328636
## 6 devices:target 0.9204901 0.08328636
## 7 block:target 0.9640826 0.33375424
## 8 devices:block:target 0.9640826 0.33375424
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 5 target 0.9263463 0.9697595 0.9541173 0.9723113
## 6 devices:target 0.9263463 0.1401996 0.9541173 0.1387575
## 7 block:target 0.9653279 0.3900901 0.9962922 0.3924769
## 8 devices:block:target 0.9653279 0.2994055 0.9962922 0.3001350
## p[HF]<.05
## 5
## 6
## 7
## 8deviceRAEPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.0429765 ±10.15%
## [2] block + participant : 8.745969 ±1%
## [3] target + block + participant : 0.3522894 ±2.2%
## [4] target + block + target:block + participant : 0.03731202 ±3.05%
## [5] devices + participant : 0.249402 ±0.84%
## [6] target + devices + participant : 0.009761271 ±1.57%
## [7] block + devices + participant : 2.179734 ±1.17%
## [8] target + block + devices + participant : 0.08852129 ±3.87%
## [9] target + block + target:block + devices + participant : 0.009827654 ±4.68%
## [10] target + devices + target:devices + participant : 0.004076451 ±3.62%
## [11] target + block + devices + target:devices + participant : 0.03907959 ±3.32%
## [12] target + block + target:block + devices + target:devices + participant : 0.004343014 ±3.3%
## [13] block + devices + block:devices + participant : 0.4124103 ±2.91%
## [14] target + block + devices + block:devices + participant : 0.01548675 ±3.14%
## [15] target + block + target:block + devices + block:devices + participant : 0.00158385 ±2.09%
## [16] target + block + devices + target:devices + block:devices + participant : 0.006994067 ±5.17%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.0007595255 ±13.95%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.0001746684 ±3.2%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.05 0.017
## block 0.74 0.90 3.25
## block:target 0.32 4.09e-03 0.009
## devices 0.74 0.23 0.106
## devices:target 0.32 4.20e-03 0.009
## block:devices 0.32 0.03 0.074
## block:devices:target 0.05 1.32e-05 2.38e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects. Overall, we only found path length differences between mouse and trackpad users in the aligned trials using the nondominant hand. This difference could be due to participants not being used to controlling the mouse with their nondominant hand, while it is easier to use the trackpad with both hands.
Sex differences: Males vs. females
We repeat the same set of analyses but now split the data according to males (N =18) and females (N = 44). Note that one participant did not identify as either male or female, so they are not included in the comparisons below.
Learning
plotSexCtrl()
The disproportionately smaller sample for males contribute to the variability we observe in their data. We first conduct a 3x3x2 (trackpad x block x sex) mixed design ANOVA, with trackpad and block as within-subjects factors and sex as a between-subjects factor, for the aligned trials for both hands.
sexAlignedLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during aligned trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.5394135 0.46553660 0.0009574108
## 3 block 2 120 0.5183481 0.59683066 0.0019129375
## 5 target 2 120 2.4567170 0.09001728 0.0091469468
## 4 sex:block 2 120 1.0032605 0.36973637 0.0036958682
## 6 sex:target 2 120 1.9289069 0.14978564 0.0071959242
## 7 block:target 4 240 1.3599332 0.24854016 0.0100097880
## 8 sex:block:target 4 240 0.1425064 0.96615417 0.0010584024
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9926280 0.8038997
## 4 sex:block 0.9926280 0.8038997
## 5 target 0.9461635 0.1954351
## 6 sex:target 0.9461635 0.1954351
## 7 block:target 0.8542897 0.4192406
## 8 sex:block:target 0.8542897 0.4192406
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9926819 0.59550997 1.0265271 0.59683066
## 4 sex:block 0.9926819 0.36928123 1.0265271 0.36973637
## 5 target 0.9489138 0.09309127 0.9790295 0.09126875
## 6 sex:target 0.9489138 0.15222886 0.9790295 0.15079004
## 7 block:target 0.9292033 0.25100875 0.9981915 0.24860439
## 8 sex:block:target 0.9292033 0.95929125 0.9981915 0.96599501
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during aligned trials across targets, blocks, and sexes, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.002146009 0.9632050 5.415639e-06
## 3 block 2 120 1.223717409 0.2977785 3.739521e-03
## 5 target 2 120 1.201195459 0.3044253 4.949721e-03
## 4 sex:block 2 120 0.195685723 0.8225325 5.998746e-04
## 6 sex:target 2 120 0.633054229 0.5327314 2.614724e-03
## 7 block:target 4 240 0.765081984 0.5488941 5.277512e-03
## 8 sex:block:target 4 240 0.116448704 0.9766073 8.068697e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9105883 0.0630958644
## 4 sex:block 0.9105883 0.0630958644
## 5 target 0.9974434 0.9272656248
## 6 sex:target 0.9974434 0.9272656248
## 7 block:target 0.5755546 0.0001799418 *
## 8 sex:block:target 0.5755546 0.0001799418 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9179266 0.2958307 0.9454884 0.2965403
## 4 sex:block 0.9179266 0.8040813 0.9454884 0.8105293
## 5 target 0.9974500 0.3043624 1.0317101 0.3044253
## 6 sex:target 0.9974500 0.5323457 1.0317101 0.5327314
## 7 block:target 0.8087236 0.5238486 0.8602493 0.5311098
## 8 sex:block:target 0.8087236 0.9585291 0.8602493 0.9645176sexAlignedLearningBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1.742858 ±1.17%
## [2] block + participant : 0.02246288 ±0.88%
## [3] target + block + participant : 0.03967097 ±1.46%
## [4] target + block + target:block + participant : 0.006741944 ±1.76%
## [5] sex + participant : 0.1578446 ±2.74%
## [6] target + sex + participant : 0.2802723 ±1.99%
## [7] block + sex + participant : 0.003427235 ±1.47%
## [8] target + block + sex + participant : 0.006111806 ±2.06%
## [9] target + block + target:block + sex + participant : 0.00104308 ±2.27%
## [10] target + sex + target:sex + participant : 0.08059277 ±1.43%
## [11] target + block + sex + target:sex + participant : 0.00191007 ±3.15%
## [12] target + block + target:block + sex + target:sex + participant : 0.0003365834 ±2.7%
## [13] block + sex + block:sex + participant : 0.0003661364 ±1.88%
## [14] target + block + sex + block:sex + participant : 0.0006779643 ±2.05%
## [15] target + block + target:block + sex + block:sex + participant : 0.0001217062 ±2.71%
## [16] target + block + sex + target:sex + block:sex + participant : 0.0002046271 ±2.67%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 3.793608e-05 ±4.08%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.290439e-06 ±3.16%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.65 0.652
## block 0.74 0.02 0.009
## block:target 0.32 2.48e-03 0.005
## sex 0.74 0.16 0.068
## sex:target 0.32 0.02 0.055
## block:sex 0.32 4.21e-04 9.14e-04
## block:sex:target 0.05 3.86e-07 6.94e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04501273 ±0.79%
## [2] block + participant : 0.07802716 ±1.22%
## [3] target + block + participant : 0.003539487 ±1.27%
## [4] target + block + target:block + participant : 9.656361e-05 ±1.32%
## [5] sex + participant : 0.1493048 ±3.5%
## [6] target + sex + participant : 0.00633829 ±1.36%
## [7] block + sex + participant : 0.01080928 ±1.54%
## [8] target + block + sex + participant : 0.0004881161 ±1.39%
## [9] target + block + target:block + sex + participant : 1.476674e-05 ±4.54%
## [10] target + sex + target:sex + participant : 0.0005693144 ±3.58%
## [11] target + block + sex + target:sex + participant : 4.670499e-05 ±6.04%
## [12] target + block + target:block + sex + target:sex + participant : 1.198659e-06 ±2.24%
## [13] block + sex + block:sex + participant : 0.000596335 ±1.86%
## [14] target + block + sex + block:sex + participant : 2.74086e-05 ±3.08%
## [15] target + block + target:block + sex + block:sex + participant : 7.349767e-07 ±2.18%
## [16] target + block + sex + target:sex + block:sex + participant : 4.891602e-06 ±52.4%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 6.795376e-08 ±5.33%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 2.017151e-09 ±5.51%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.04 0.016
## block 0.74 0.07 0.028
## block:target 0.32 8.75e-05 1.90e-04
## sex 0.74 0.13 0.053
## sex:target 0.32 4.80e-04 0.001
## block:sex 0.32 4.86e-04 0.001
## block:sex:target 0.05 1.56e-09 2.80e-08
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any sex-related effects. Next, we conduct the same test for mirror reversed reaches.
sexmirrorANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.8275751 0.36661468 0.0013625906
## 3 target 2 120 2.9845908 0.05432707 0.0091593619
## 5 block 2 120 0.3289519 0.72032453 0.0012868471
## 4 sex:target 2 120 0.2645141 0.76802520 0.0008185963
## 6 sex:block 2 120 0.8985704 0.40987284 0.0035073572
## 7 target:block 4 240 0.8061139 0.52230378 0.0064105181
## 8 sex:target:block 4 240 1.1562535 0.33085051 0.0091694264
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.076435424 1.140757e-33 *
## 4 sex:target 0.076435424 1.140757e-33 *
## 5 block 0.793782277 1.099490e-03 *
## 6 sex:block 0.793782277 1.099490e-03 *
## 7 target:block 0.001309785 1.054189e-77 *
## 8 sex:target:block 0.001309785 1.054189e-77 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.5198682 0.08759622 0.5208925 0.08751342
## 4 sex:target 0.5198682 0.61804793 0.5208925 0.61850889
## 5 block 0.8290377 0.67961611 0.8496686 0.68499075
## 6 sex:block 0.8290377 0.39365414 0.8496686 0.39581388
## 7 target:block 0.4234870 0.43111343 0.4344782 0.43388555
## 8 sex:target:block 0.4234870 0.31223629 0.4344782 0.31321850
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8sexmirrorBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.2184337 ±1.97%
## [2] block + participant : 0.02927938 ±1.36%
## [3] target + block + participant : 0.006163188 ±1.14%
## [4] target + block + target:block + participant : 0.0001694851 ±1.66%
## [5] sex + participant : 0.1674023 ±1.71%
## [6] target + sex + participant : 0.03507489 ±1.4%
## [7] block + sex + participant : 0.004728268 ±1.56%
## [8] target + block + sex + participant : 0.001001409 ±1.67%
## [9] target + block + target:block + sex + participant : 2.800976e-05 ±1.95%
## [10] target + sex + target:sex + participant : 0.001879392 ±1.94%
## [11] target + block + sex + target:sex + participant : 5.355698e-05 ±2.04%
## [12] target + block + target:block + sex + target:sex + participant : 1.546404e-06 ±3.33%
## [13] block + sex + block:sex + participant : 0.0005103473 ±1.98%
## [14] target + block + sex + block:sex + participant : 0.0001115286 ±2.56%
## [15] target + block + target:block + sex + block:sex + participant : 2.97633e-06 ±2%
## [16] target + block + sex + target:sex + block:sex + participant : 6.754722e-06 ±8.54%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1.723687e-07 ±5.57%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 2.496298e-08 ±2.18%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.18 0.078
## block 0.74 0.03 0.011
## block:target 0.32 1.38e-04 2.99e-04
## sex 0.74 0.14 0.060
## sex:target 0.32 1.33e-03 0.003
## block:sex 0.32 4.31e-04 9.35e-04
## block:sex:target 0.05 1.70e-08 3.07e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalThere are no sex-related effects. Finally, we test washout trials.
RAESexLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during washout trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.54789267 0.4620667 0.0015796592
## 3 block 1 60 1.71433698 0.1954156 0.0043990971
## 5 target 2 120 0.03515675 0.9654640 0.0002175041
## 4 sex:block 1 60 1.27958189 0.2624780 0.0032871553
## 6 sex:target 2 120 0.14082482 0.8687848 0.0008706709
## 7 block:target 2 120 0.32302586 0.7245827 0.0016168744
## 8 sex:block:target 2 120 0.31673716 0.7291294 0.0015854469
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9268801 0.1064622
## 6 sex:target 0.9268801 0.1064622
## 7 block:target 0.9820799 0.5865858
## 8 sex:block:target 0.9820799 0.5865858
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 5 target 0.9318623 0.9582006 0.9605638 0.9614379
## 6 sex:target 0.9318623 0.8547447 0.9605638 0.8608600
## 7 block:target 0.9823954 0.7207491 1.0153512 0.7245827
## 8 sex:block:target 0.9823954 0.7252856 1.0153512 0.7291294RAESexLearningBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.02964391 ±0.76%
## [2] block + participant : 0.172626 ±2.92%
## [3] target + block + participant : 0.004968513 ±1.35%
## [4] target + block + target:block + participant : 0.0004974946 ±3.28%
## [5] sex + participant : 0.1894066 ±0.91%
## [6] target + sex + participant : 0.005581734 ±1.43%
## [7] block + sex + participant : 0.03114729 ±1.14%
## [8] target + block + sex + participant : 0.001052129 ±6.62%
## [9] target + block + target:block + sex + participant : 8.894752e-05 ±2.79%
## [10] target + sex + target:sex + participant : 0.0004308518 ±7.96%
## [11] target + block + sex + target:sex + participant : 7.408793e-05 ±3.18%
## [12] target + block + target:block + sex + target:sex + participant : 6.225295e-06 ±2.36%
## [13] block + sex + block:sex + participant : 0.009435529 ±1.83%
## [14] target + block + sex + block:sex + participant : 0.0003029393 ±5.37%
## [15] target + block + target:block + sex + block:sex + participant : 2.747651e-05 ±4.63%
## [16] target + block + sex + target:sex + block:sex + participant : 2.324283e-05 ±7.79%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2.024986e-06 ±4.66%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 2.941845e-07 ±4.74%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.011
## block 0.74 0.15 0.064
## block:target 0.32 4.31e-04 9.34e-04
## sex 0.74 0.16 0.070
## sex:target 0.32 3.71e-04 8.05e-04
## block:sex 0.32 6.77e-03 0.015
## block:sex:target 0.05 2.04e-07 3.66e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find sex-related effects. Overall, learning the mirror reversal did not differ between males and females.
Completion time
plotSexCtrlMT()
Next, we test for sex-related effects with completion times across the different trial types. First, we test aligned trials.
sexAlignedMTANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during aligned trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 2.2021472 0.1430532306 2.969647e-02
## 3 block 2 120 9.0187512 0.0002244136 * 1.225824e-02
## 5 target 2 120 1.7433813 0.1793289676 1.917954e-03
## 4 sex:block 2 120 0.2656396 0.7671650667 3.654033e-04
## 6 sex:target 2 120 0.9708498 0.3817158057 1.068974e-03
## 7 block:target 4 240 0.2303513 0.9211706842 6.688927e-05
## 8 sex:block:target 4 240 0.3583436 0.8380808119 1.040517e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.3040596 5.588324e-16 *
## 4 sex:block 0.3040596 5.588324e-16 *
## 5 target 0.2836304 7.181339e-17 *
## 6 sex:target 0.2836304 7.181339e-17 *
## 7 block:target 0.6123178 7.450152e-04 *
## 8 sex:block:target 0.6123178 7.450152e-04 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.5896434 0.002326023 * 0.5944886 0.00226224
## 4 sex:block 0.5896434 0.646734641 0.5944886 0.64864648
## 5 target 0.5826251 0.191315630 0.5870702 0.19126152
## 6 sex:target 0.5826251 0.341125195 0.5870702 0.34174315
## 7 block:target 0.8133906 0.889208922 0.8655491 0.89941463
## 8 sex:block:target 0.8133906 0.799129386 0.8655491 0.81112612
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during aligned trials across targets, blocks, and sexes, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 1.89336313 0.17393760 0.0212560059
## 3 block 2 120 3.18926540 0.04471741 * 0.0089489377
## 5 target 2 120 2.09754016 0.12723635 0.0017911183
## 4 sex:block 2 120 1.47278547 0.23340034 0.0041525712
## 6 sex:target 2 120 0.37050764 0.69117076 0.0003168488
## 7 block:target 4 240 0.06558589 0.99205900 0.0000989938
## 8 sex:block:target 4 240 0.49086625 0.74245350 0.0007404267
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.4467670 4.757650e-11 *
## 4 sex:block 0.4467670 4.757650e-11 *
## 5 target 0.9818769 5.830191e-01
## 6 sex:target 0.9818769 5.830191e-01
## 7 block:target 0.2692337 7.714761e-13 *
## 8 sex:block:target 0.2692337 7.714761e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6438184 0.06753798 0.6518716 0.06692397
## 4 sex:block 0.6438184 0.23393812 0.6518716 0.23406480
## 5 target 0.9821995 0.12820063 1.0151384 0.12723635
## 6 sex:target 0.9821995 0.68740068 1.0151384 0.69117076
## 7 block:target 0.5886319 0.95674519 0.6142121 0.96121091
## 8 sex:block:target 0.5886319 0.64377365 0.6142121 0.65172485
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8sexAlignedMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 2.90022 ±1.76%
## [2] block + participant : 139365844 ±0.7%
## [3] target + block + participant : 647835499 ±1.17%
## [4] target + block + target:block + participant : 5804497 ±2.11%
## [5] sex + participant : 0.8456109 ±2.02%
## [6] target + sex + participant : 2.634413 ±3.91%
## [7] block + sex + participant : 146064408 ±17.34%
## [8] target + block + sex + participant : 544356514 ±3.33%
## [9] target + block + target:block + sex + participant : 4874000 ±6.69%
## [10] target + sex + target:sex + participant : 0.4113752 ±2.38%
## [11] target + block + sex + target:sex + participant : 166742883 ±36.24%
## [12] target + block + target:block + sex + target:sex + participant : 958132.1 ±2.92%
## [13] block + sex + block:sex + participant : 9657410 ±5.09%
## [14] target + block + sex + block:sex + participant : 41663266 ±2.48%
## [15] target + block + target:block + sex + block:sex + participant : 417319.8 ±6.97%
## [16] target + block + sex + target:sex + block:sex + participant : 8849925 ±2.75%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 75588.38 ±3.72%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 2765.95 ±12.29%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.83 1.72
## block 0.74 1.00 7.87e+07
## block:target 0.32 7.07e-03 0.015
## sex 0.74 0.54 0.416
## sex:target 0.32 0.10 0.248
## block:sex 0.32 0.04 0.079
## block:sex:target 0.05 1.61e-06 2.90e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.08146741 ±0.91%
## [2] block + participant : 6988.79 ±0.5%
## [3] target + block + participant : 633.8235 ±1.77%
## [4] target + block + target:block + participant : 6.43274 ±3%
## [5] sex + participant : 0.7117176 ±1.01%
## [6] target + sex + participant : 0.0586529 ±2.22%
## [7] block + sex + participant : 5261.868 ±1.79%
## [8] target + block + sex + participant : 457.7214 ±2.8%
## [9] target + block + target:block + sex + participant : 4.359247 ±1.84%
## [10] target + sex + target:sex + participant : 0.003472687 ±5.38%
## [11] target + block + sex + target:sex + participant : 24.88377 ±2.01%
## [12] target + block + target:block + sex + target:sex + participant : 0.2508262 ±4.11%
## [13] block + sex + block:sex + participant : 5319.129 ±3.19%
## [14] target + block + sex + block:sex + participant : 456.5556 ±2%
## [15] target + block + target:block + sex + block:sex + participant : 4.881957 ±4.6%
## [16] target + block + sex + target:sex + block:sex + participant : 24.04146 ±1.87%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.2969208 ±9.41%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.009918473 ±3.36%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.08 0.033
## block 0.74 1.00 3.69e+03
## block:target 0.32 8.46e-04 0.002
## sex 0.74 0.60 0.541
## sex:target 0.32 2.58e-03 0.006
## block:sex 0.32 0.30 0.940
## block:sex:target 0.05 5.17e-07 9.31e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects of sex. We then look into the mirror reversed trials.
sexMirrorMTANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 5.9896694 1.733418e-02 * 0.027182747
## 3 target 2 120 18.0469373 1.405151e-07 * 0.052389471
## 5 block 2 120 27.4560573 1.519432e-10 * 0.096076317
## 4 sex:target 2 120 1.1586491 3.173964e-01 0.003536908
## 6 sex:block 2 120 2.4102089 9.413191e-02 0.009244166
## 7 target:block 4 240 2.7224775 3.022458e-02 * 0.013606899
## 8 sex:target:block 4 240 0.2782311 8.918903e-01 0.001407793
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9418537 1.708096e-01
## 4 sex:target 0.9418537 1.708096e-01
## 5 block 0.6152843 5.994272e-07 *
## 6 sex:block 0.6152843 5.994272e-07 *
## 7 target:block 0.2605728 3.233792e-13 *
## 8 sex:target:block 0.2605728 3.233792e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.9450489 2.795514e-07 * 0.9748422 1.925078e-07
## 4 sex:target 0.9450489 3.155323e-01 0.9748422 3.165718e-01
## 5 block 0.7221699 3.062291e-08 * 0.7352383 2.384339e-08
## 6 sex:block 0.7221699 1.115805e-01 0.7352383 1.107256e-01
## 7 target:block 0.5677428 6.225575e-02 0.5912504 5.983768e-02
## 8 sex:target:block 0.5677428 7.849100e-01 0.5912504 7.934334e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8sexMirrorMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 2257101 ±1.8%
## [2] block + participant : 4.301375e+16 ±0.57%
## [3] target + block + participant : 3.498992e+24 ±1.43%
## [4] target + block + target:block + participant : 1.59181e+24 ±1.59%
## [5] sex + participant : 1.858008 ±1.36%
## [6] target + sex + participant : 4223992 ±1.16%
## [7] block + sex + participant : 8.950176e+16 ±1.24%
## [8] target + block + sex + participant : 7.528669e+24 ±1.51%
## [9] target + block + target:block + sex + participant : 3.968591e+24 ±10.4%
## [10] target + sex + target:sex + participant : 468823.5 ±1.47%
## [11] target + block + sex + target:sex + participant : 1.060162e+24 ±2.49%
## [12] target + block + target:block + sex + target:sex + participant : 4.823576e+23 ±2.13%
## [13] block + sex + block:sex + participant : 6.514598e+16 ±4.96%
## [14] target + block + sex + block:sex + participant : 6.707684e+24 ±2.36%
## [15] target + block + target:block + sex + block:sex + participant : 3.453736e+24 ±4.74%
## [16] target + block + sex + target:sex + block:sex + participant : 9.253307e+23 ±2.29%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 5.212821e+23 ±9.77%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.563753e+22 ±2.02%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.38e+07
## block 0.74 1.00 1.53e+18
## block:target 0.32 0.34 1.10
## sex 0.74 0.83 1.73
## sex:target 0.32 0.10 0.243
## block:sex 0.32 0.39 1.39
## block:sex:target 0.05 5.26e-04 0.009
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of sex.
sexMirrorMTComparisons()##
## Welch Two Sample t-test
##
## data: maledat$movementtime and femaledat$movementtime
## t = -2.9857, df = 50.912, p-value = 0.004341
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2.2282246 -0.4364219
## sample estimates:
## mean of x mean of y
## 3.002728 4.335052
##
## Bayesian t-test (males vs. females):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.118012 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up tests show that regardless of target or block, males have faster completion times on average during perturbed reaches.
Finally, we test for washout trials.
sexRAEMTANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during washout trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 4.508826280 3.785353e-02 * 5.435103e-02
## 3 block 1 60 30.725790132 7.014811e-07 * 1.551028e-02
## 5 target 2 120 3.361268454 3.798772e-02 * 5.992622e-03
## 4 sex:block 1 60 4.048671616 4.870218e-02 * 2.071654e-03
## 6 sex:target 2 120 0.032127960 9.683910e-01 5.762118e-05
## 7 block:target 2 120 0.006046689 9.939719e-01 9.754048e-06
## 8 sex:block:target 2 120 0.359008560 6.991159e-01 5.787951e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9970279 0.9159372
## 6 sex:target 0.9970279 0.9159372
## 7 block:target 0.9351011 0.1381428
## 8 sex:block:target 0.9351011 0.1381428
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 5 target 0.9970367 0.03813335 * 1.0312608 0.03798772
## 6 sex:target 0.9970367 0.96812031 1.0312608 0.96839099
## 7 block:target 0.9390563 0.99205112 0.9683518 0.99304194
## 8 sex:block:target 0.9390563 0.68578941 0.9683518 0.69230775
## p[HF]<.05
## 5 *
## 6
## 7
## 8sexRAEMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1.94029 ±0.98%
## [2] block + participant : 268702.2 ±1.17%
## [3] target + block + participant : 816439.4 ±1.95%
## [4] target + block + target:block + participant : 49985.05 ±2.12%
## [5] sex + participant : 1.955497 ±2.5%
## [6] target + sex + participant : 3.679175 ±2.65%
## [7] block + sex + participant : 505847.7 ±2.38%
## [8] target + block + sex + participant : 1470903 ±2.14%
## [9] target + block + target:block + sex + participant : 93321.23 ±3.92%
## [10] target + sex + target:sex + participant : 0.244633 ±2.58%
## [11] target + block + sex + target:sex + participant : 109880.6 ±6.13%
## [12] target + block + target:block + sex + target:sex + participant : 6246.472 ±3.46%
## [13] block + sex + block:sex + participant : 311712.1 ±2.98%
## [14] target + block + sex + block:sex + participant : 1097776 ±8.45%
## [15] target + block + target:block + sex + block:sex + participant : 64602.95 ±5.6%
## [16] target + block + sex + target:sex + block:sex + participant : 71968.14 ±5.48%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 3967.992 ±4.24%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 621.6262 ±5.4%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.78 1.24
## block 0.74 1.00 1.97e+05
## block:target 0.32 0.04 0.102
## sex 0.74 0.77 1.18
## sex:target 0.32 0.04 0.089
## block:sex 0.32 0.32 1.01
## block:sex:target 0.05 1.28e-04 0.002
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of sex and a sex x block interaction.
sexRAEMTComparisonsEffSize()## Contrasts set to contr.sum for the following variables: sex## contrast estimate SE df t.ratio p.value
## 1st block: Males vs Females -0.449 0.1930 60 -2.328 0.0699
## 2nd block: Males vs Females -0.306 0.1689 60 -1.811 0.2255
## Last block: Males vs Females -0.169 0.0865 60 -1.955 0.1657
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 1st block: Males vs Females 0.08282991
## 2 2nd block: Males vs Females 0.05182093
## 3 Last block: Males vs Females 0.05989916sexRAEMTBayesfollowup()## Bayesian t-test block 1, males vs females:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.490646 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2, males vs females:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.063017 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block, males vs females:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.321738 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up frequentist tests do not show any significant effects. But Bayesian tests show anecdotal evidence that males continue to move faster after perturbation training. These results suggest that males initiate and execute movements faster than females during perturbed and washout trials, even though no sex differences were observed in aligned baseline reaches.
Path length
plotSexCtrlPL()
We repeat the same tests and use path length as the dependent variable.
sexAlignedPLANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during aligned trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.04799516 0.82733286 0.0004186358
## 3 block 2 120 0.59190991 0.55487671 0.0015089908
## 5 target 2 120 7.27115819 0.00104554 * 0.0157779940
## 4 sex:block 2 120 1.78914909 0.17153082 0.0045473038
## 6 sex:target 2 120 0.59201121 0.55482106 0.0013035226
## 7 block:target 4 240 0.27117840 0.89636587 0.0008623122
## 8 sex:block:target 4 240 1.29914014 0.27103257 0.0041176377
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8295732 0.004038441 *
## 4 sex:block 0.8295732 0.004038441 *
## 5 target 0.9699288 0.406279674
## 6 sex:target 0.9699288 0.406279674
## 7 block:target 0.7131488 0.019576145 *
## 8 sex:block:target 0.7131488 0.019576145 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8543892 0.529537703 0.8769372 0.53371897
## 4 sex:block 0.8543892 0.177210794 0.8769372 0.17636577
## 5 target 0.9708066 0.001185024 * 1.0027699 0.00104554
## 6 sex:target 0.9708066 0.550036732 1.0027699 0.55482106
## 7 block:target 0.8659100 0.872323502 0.9254312 0.88371551
## 8 sex:block:target 0.8659100 0.274160596 0.9254312 0.27284544
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during aligned trials across targets, blocks, and sexes, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 1.72263552 0.194352779 0.0087593988
## 3 block 2 120 6.40857463 0.002267908 * 0.0166185711
## 5 target 2 120 0.87333916 0.420191733 0.0025962877
## 4 sex:block 2 120 0.77180172 0.464459974 0.0020311078
## 6 sex:target 2 120 0.06131514 0.940556241 0.0001827205
## 7 block:target 4 240 1.13296414 0.341571614 0.0066616595
## 8 sex:block:target 4 240 1.36704257 0.246019135 0.0080269578
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9540306 0.249510212
## 4 sex:block 0.9540306 0.249510212
## 5 target 0.8504614 0.008410302 *
## 6 sex:target 0.8504614 0.008410302 *
## 7 block:target 0.6301317 0.001416781 *
## 8 sex:block:target 0.6301317 0.001416781 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9560509 0.002658413 * 0.9867650 0.002378985
## 4 sex:block 0.9560509 0.459261355 0.9867650 0.462919652
## 5 target 0.8699143 0.407396820 0.8936598 0.409890586
## 6 sex:target 0.8699143 0.920068310 0.8936598 0.924311773
## 7 block:target 0.8048958 0.338516717 0.8559051 0.339564154
## 8 sex:block:target 0.8048958 0.252737839 0.8559051 0.251086272
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8sexAlignedPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 157.9005 ±0.77%
## [2] block + participant : 0.04893224 ±0.93%
## [3] target + block + participant : 8.179717 ±1.81%
## [4] target + block + target:block + participant : 0.06766173 ±5.07%
## [5] sex + participant : 0.2802199 ±0.64%
## [6] target + sex + participant : 44.67152 ±0.94%
## [7] block + sex + participant : 0.01362527 ±1.39%
## [8] target + block + sex + participant : 2.304002 ±2.89%
## [9] target + block + target:block + sex + participant : 0.01808761 ±2.32%
## [10] target + sex + target:sex + participant : 4.142017 ±5.76%
## [11] target + block + sex + target:sex + participant : 0.181064 ±1.52%
## [12] target + block + target:block + sex + target:sex + participant : 0.001505487 ±3.38%
## [13] block + sex + block:sex + participant : 0.004672782 ±2.46%
## [14] target + block + sex + block:sex + participant : 0.8048356 ±2.1%
## [15] target + block + target:block + sex + block:sex + participant : 0.006411949 ±2.32%
## [16] target + block + sex + target:sex + block:sex + participant : 0.06861571 ±2.46%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.000582017 ±10.62%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 6.197625e-05 ±7.58%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.99 57.87
## block 0.74 0.05 0.020
## block:target 0.32 4.29e-04 9.31e-04
## sex 0.74 0.24 0.112
## sex:target 0.32 0.02 0.044
## block:sex 0.32 4.03e-03 0.009
## block:sex:target 0.05 2.82e-07 5.08e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04723258 ±0.66%
## [2] block + participant : 3.070284 ±1.32%
## [3] target + block + participant : 0.1471664 ±1.22%
## [4] target + block + target:block + participant : 0.00442739 ±1.96%
## [5] sex + participant : 0.3989471 ±1.29%
## [6] target + sex + participant : 0.01933883 ±2.34%
## [7] block + sex + participant : 1.228319 ±1.67%
## [8] target + block + sex + participant : 0.05851282 ±1.5%
## [9] target + block + target:block + sex + participant : 0.001826601 ±2.1%
## [10] target + sex + target:sex + participant : 0.0008761342 ±2.97%
## [11] target + block + sex + target:sex + participant : 0.002847506 ±3.37%
## [12] target + block + target:block + sex + target:sex + participant : 8.318111e-05 ±2.56%
## [13] block + sex + block:sex + participant : 0.09374514 ±1.29%
## [14] target + block + sex + block:sex + participant : 0.004820329 ±3.91%
## [15] target + block + target:block + sex + block:sex + participant : 0.000141499 ±2.16%
## [16] target + block + sex + target:sex + block:sex + participant : 0.0002213503 ±4.13%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 6.550628e-06 ±2.31%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.184635e-06 ±2.93%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.05 0.018
## block 0.74 0.76 1.12
## block:target 0.32 1.07e-03 0.002
## sex 0.74 0.30 0.151
## sex:target 0.32 6.64e-04 0.001
## block:sex 0.32 0.02 0.036
## block:sex:target 0.05 1.95e-07 3.51e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find sex-related effects in the aligned trials. Next, we test for mirror reversed trials.
sexMirrorPLANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 1.98923864 1.635840e-01 5.899935e-03
## 3 target 2 120 16.84584604 3.563291e-07 * 5.507236e-02
## 5 block 2 120 21.45024441 1.085254e-08 * 9.259100e-02
## 4 sex:target 2 120 0.01053895 9.895173e-01 3.646061e-05
## 6 sex:block 2 120 0.69385260 5.016406e-01 3.289801e-03
## 7 target:block 4 240 3.56430419 7.597503e-03 * 1.911156e-02
## 8 sex:target:block 4 240 0.27177039 8.959922e-01 1.483403e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9984915 9.564418e-01
## 4 sex:target 0.9984915 9.564418e-01
## 5 block 0.3847823 5.805569e-13 *
## 6 sex:block 0.3847823 5.805569e-13 *
## 7 target:block 0.1616070 8.206911e-19 *
## 8 sex:target:block 0.1616070 8.206911e-19 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.9984937 3.626262e-07 * 1.0328449 3.563291e-07
## 4 sex:target 0.9984937 9.894543e-01 1.0328449 9.895173e-01
## 5 block 0.6191116 3.302074e-06 * 0.6256755 2.990767e-06
## 6 sex:block 0.6191116 4.369205e-01 0.6256755 4.383413e-01
## 7 target:block 0.6437578 2.075810e-02 * 0.6751284 1.898072e-02
## 8 sex:target:block 0.6437578 8.157610e-01 0.6751284 8.252954e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8sexMirrorPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 586658.2 ±1.81%
## [2] block + participant : 4.445859e+13 ±0.96%
## [3] target + block + participant : 3.431267e+20 ±1.28%
## [4] target + block + target:block + participant : 7.289525e+20 ±1.23%
## [5] sex + participant : 0.2804267 ±1.04%
## [6] target + sex + participant : 173961 ±4.46%
## [7] block + sex + participant : 1.395905e+13 ±4.38%
## [8] target + block + sex + participant : 1.119556e+20 ±2.4%
## [9] target + block + target:block + sex + participant : 2.543613e+20 ±5.88%
## [10] target + sex + target:sex + participant : 7499.468 ±1.32%
## [11] target + block + sex + target:sex + participant : 5.308787e+18 ±4.4%
## [12] target + block + target:block + sex + target:sex + participant : 1.213373e+19 ±4.77%
## [13] block + sex + block:sex + participant : 1.553397e+12 ±3.2%
## [14] target + block + sex + block:sex + participant : 1.284453e+19 ±2.5%
## [15] target + block + target:block + sex + block:sex + participant : 2.945013e+19 ±2.64%
## [16] target + block + sex + target:sex + block:sex + participant : 6.13778e+17 ±3.03%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1.334621e+18 ±2.68%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 4.86856e+16 ±2.68%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 8.93e+06
## block 0.74 1.00 6.97e+14
## block:target 0.32 0.68 4.69
## sex 0.74 0.29 0.143
## sex:target 0.32 0.01 0.028
## block:sex 0.32 0.03 0.066
## block:sex:target 0.05 3.25e-05 5.84e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalThere are no sex-related effects. Finally, we test for washout trials.
sexRAEPLANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during washout trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.7856525 0.378956919 0.0048381922
## 3 block 1 60 7.9731922 0.006433612 * 0.0193479645
## 5 target 2 120 0.3712295 0.690675062 0.0017366603
## 4 sex:block 1 60 0.4512855 0.504303603 0.0011154621
## 6 sex:target 2 120 2.3719627 0.097658573 0.0109934569
## 7 block:target 2 120 0.2192692 0.803426566 0.0007269559
## 8 sex:block:target 2 120 1.4828557 0.231117676 0.0048956890
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9562554 0.2672578
## 6 sex:target 0.9562554 0.2672578
## 7 block:target 0.9668903 0.3703628
## 8 sex:block:target 0.9668903 0.3703628
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 5 target 0.9580888 0.6816858 0.9889745 0.68834962
## 6 sex:target 0.9580888 0.1001503 0.9889745 0.09830931
## 7 block:target 0.9679514 0.7963709 0.9996717 0.80335586
## 8 sex:block:target 0.9679514 0.2315547 0.9996717 0.23112237sexRAEPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.04069975 ±3.18%
## [2] block + participant : 9.351155 ±2.83%
## [3] target + block + participant : 0.4175703 ±11.41%
## [4] target + block + target:block + participant : 0.04374696 ±2.31%
## [5] sex + participant : 0.2899085 ±1.2%
## [6] target + sex + participant : 0.01190957 ±4.27%
## [7] block + sex + participant : 2.782138 ±1.79%
## [8] target + block + sex + participant : 0.1280074 ±16.9%
## [9] target + block + target:block + sex + participant : 0.01359755 ±5.01%
## [10] target + sex + target:sex + participant : 0.006589562 ±1.43%
## [11] target + block + sex + target:sex + participant : 0.06599999 ±1.64%
## [12] target + block + target:block + sex + target:sex + participant : 0.008107844 ±2.83%
## [13] block + sex + block:sex + participant : 0.6203291 ±7.92%
## [14] target + block + sex + block:sex + participant : 0.0218964 ±1.73%
## [15] target + block + target:block + sex + block:sex + participant : 0.002628508 ±2.44%
## [16] target + block + sex + target:sex + block:sex + participant : 0.01479356 ±3.22%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.002868784 ±38.95%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.000510278 ±4.2%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.05 0.020
## block 0.74 0.91 3.57
## block:target 0.32 4.82e-03 0.010
## sex 0.74 0.27 0.131
## sex:target 0.32 6.67e-03 0.015
## block:sex 0.32 0.04 0.101
## block:sex:target 0.05 3.44e-05 6.20e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any sex effects. Thus, although males move faster than females, the overall trajectory of their reaches do not differ.
Session 2
We also conducted tests that compared device used and sex for reaches in the second session.
Device used: Mouse vs. trackpad
In session 2, there were less mouse users (N = 9) than trackpad users (n = 39), which is probably contributing to the large variability observed in the plots.
Learning
plotDeviceCtrlGen()
We test for device effects for reaches within each quadrant. We conduct a 3x3x2 (target x block x device) mixed design ANOVA, with target and block as within-subjects factors and device as a between-subjects factor. We repeat this test for quadrants 1, 4, 2, top up quadrant 1 trials, and quadrant 1 trials after switching hands.
deviceLearningGenANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 1.330208 0.254726046 0.003461476
## 3 block 2 92 2.948688 0.057381494 0.014433018
## 5 target 2 92 2.474888 0.089760801 0.010834423
## 4 devices:block 2 92 4.160985 0.018621806 * 0.020246739
## 6 devices:target 2 92 1.256262 0.289553787 0.005529090
## 7 block:target 4 184 1.583587 0.180457867 0.015183372
## 8 devices:block:target 4 184 3.552583 0.008094556 * 0.033430910
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.982793014 6.767003e-01
## 4 devices:block 0.982793014 6.767003e-01
## 5 target 0.092825241 5.922252e-24 *
## 6 devices:target 0.092825241 5.922252e-24 *
## 7 block:target 0.003951147 1.250558e-47 *
## 8 devices:block:target 0.003951147 1.250558e-47 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9830841 0.05834923 1.0265959 0.05738149
## 4 devices:block 0.9830841 0.01921712 * 1.0265959 0.01862181
## 5 target 0.5243358 0.12096518 0.5259863 0.12085763
## 6 devices:target 0.5243358 0.27029060 0.5259863 0.27042724
## 7 block:target 0.5041984 0.21057112 0.5274132 0.20937673
## 8 devices:block:target 0.5041984 0.03225865 * 0.5274132 0.03020674
## p[HF]<.05
## 3
## 4 *
## 5
## 6
## 7
## 8 *## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.04872535 0.826273142 1.291908e-04
## 3 block 2 92 0.46301023 0.630844712 2.318659e-03
## 5 target 2 92 5.16511997 0.007482667 * 2.042594e-02
## 4 devices:block 2 92 0.57200009 0.566389682 2.862895e-03
## 6 devices:target 2 92 0.01226795 0.987808614 4.952388e-05
## 7 block:target 4 184 0.57955171 0.677821493 5.779823e-03
## 8 devices:block:target 4 184 0.49254800 0.741215962 4.916408e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.767993721 2.633586e-03 *
## 4 devices:block 0.767993721 2.633586e-03 *
## 5 target 0.100554236 3.581033e-23 *
## 6 devices:target 0.100554236 3.581033e-23 *
## 7 block:target 0.002566977 1.192826e-51 *
## 8 devices:block:target 0.002566977 1.192826e-51 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8116842 0.59090316 0.8371333 0.59679797
## 4 devices:block 0.8116842 0.53192084 0.8371333 0.53699867
## 5 target 0.5264694 0.02590876 * 0.5282672 0.02578723
## 6 devices:target 0.5264694 0.92133510 0.5282672 0.92191264
## 7 block:target 0.4272519 0.53646997 0.4420953 0.54203772
## 8 devices:block:target 0.4272519 0.58361539 0.4420953 0.58991168
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 2.5963688 0.11395017 0.0079277312
## 3 block 2 92 0.8429957 0.43371640 0.0037671041
## 5 target 2 92 4.4487713 0.01431308 * 0.0211985267
## 4 devices:block 2 92 0.5118169 0.60110207 0.0022905518
## 6 devices:target 2 92 4.5259919 0.01334066 * 0.0215585523
## 7 block:target 4 184 0.1997769 0.93822030 0.0018559732
## 8 devices:block:target 4 184 0.1032470 0.98125066 0.0009600489
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.983837166 6.930627e-01
## 4 devices:block 0.983837166 6.930627e-01
## 5 target 0.071224721 1.528242e-26 *
## 6 devices:target 0.071224721 1.528242e-26 *
## 7 block:target 0.007907931 3.522223e-41 *
## 8 devices:block:target 0.007907931 3.522223e-41 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9840942 0.43215025 1.0277213 0.43371640
## 4 devices:block 0.9840942 0.59820450 1.0277213 0.60110207
## 5 target 0.5184637 0.03890096 * 0.5197108 0.03880159
## 6 devices:target 0.5184637 0.03729631 * 0.5197108 0.03719824
## 7 block:target 0.5157395 0.82579063 0.5403131 0.83541376
## 8 devices:block:target 0.5157395 0.90727759 0.5403131 0.91489112
## p[HF]<.05
## 3
## 4
## 5 *
## 6 *
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.5082008 0.4795196 0.001478362
## 3 block 2 92 2.0452209 0.1351921 0.009710985
## 5 target 2 92 0.3619086 0.6973329 0.001727559
## 4 devices:block 2 92 0.6428260 0.5281495 0.003072685
## 6 devices:target 2 92 1.6127809 0.2049166 0.007652862
## 7 block:target 4 184 1.2646127 0.2855420 0.011561657
## 8 devices:block:target 4 184 0.5672237 0.6867416 0.005219090
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.987124015 7.470741e-01
## 4 devices:block 0.987124015 7.470741e-01
## 5 target 0.062099394 6.989814e-28 *
## 6 devices:target 0.062099394 6.989814e-28 *
## 7 block:target 0.002865018 1.262857e-50 *
## 8 devices:block:target 0.002865018 1.262857e-50 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9872877 0.1358639 1.0312796 0.1351921
## 4 devices:block 0.9872877 0.5262566 1.0312796 0.5281495
## 5 target 0.5160223 0.5570290 0.5171027 0.5574689
## 6 devices:target 0.5160223 0.2108032 0.5171027 0.2108223
## 7 block:target 0.5076160 0.2874178 0.5312303 0.2879784
## 8 devices:block:target 0.5076160 0.5715974 0.5312303 0.5792159
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.1781590 0.6749264 0.0006773170
## 3 block 2 92 1.6400652 0.1995870 0.0063146349
## 5 target 2 92 0.1215263 0.8857097 0.0007183433
## 4 devices:block 2 92 1.8310712 0.1660333 0.0070448720
## 6 devices:target 2 92 0.1407921 0.8688567 0.0008321292
## 7 block:target 4 184 0.5749000 0.6811837 0.0046606423
## 8 devices:block:target 4 184 1.0698033 0.3728353 0.0086381048
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.937915844 2.364216e-01
## 4 devices:block 0.937915844 2.364216e-01
## 5 target 0.068033628 5.448560e-27 *
## 6 devices:target 0.068033628 5.448560e-27 *
## 7 block:target 0.002063054 1.087201e-53 *
## 8 devices:block:target 0.002063054 1.087201e-53 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9415450 0.2012794 0.9804090 0.2001655
## 4 devices:block 0.9415450 0.1685378 0.9804090 0.1668776
## 5 target 0.5176074 0.7378274 0.5187959 0.7384117
## 6 devices:target 0.5176074 0.7180403 0.5187959 0.7186230
## 7 block:target 0.4630895 0.5521154 0.4816839 0.5586056
## 8 devices:block:target 0.4630895 0.3435267 0.4816839 0.3454901
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8deviceLearningGenBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.07527833 ±0.63%
## [2] block + participant : 0.0414189 ±0.59%
## [3] target + block + participant : 0.003863438 ±18.31%
## [4] target + block + target:block + participant : 3.987539e-05 ±5.68%
## [5] devices + participant : 0.2614151 ±1.45%
## [6] target + devices + participant : 0.01953786 ±1.49%
## [7] block + devices + participant : 0.01041409 ±1.24%
## [8] target + block + devices + participant : 0.0008126512 ±2.41%
## [9] target + block + target:block + devices + participant : 9.815617e-06 ±3.15%
## [10] target + devices + target:devices + participant : 0.003752501 ±10.16%
## [11] target + block + devices + target:devices + participant : 0.0001370842 ±2.14%
## [12] target + block + target:block + devices + target:devices + participant : 2.481046e-06 ±26.81%
## [13] block + devices + block:devices + participant : 0.02607584 ±1.43%
## [14] target + block + devices + block:devices + participant : 0.002051934 ±1.96%
## [15] target + block + target:block + devices + block:devices + participant : 2.423051e-05 ±2.18%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0003567985 ±2.62%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3.999572e-06 ±2.22%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1.745809e-05 ±2.89%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.07 0.028
## block 0.74 0.06 0.022
## block:target 0.32 6.77e-05 1.47e-04
## devices 0.74 0.22 0.103
## devices:target 0.32 2.95e-03 0.006
## block:devices 0.32 0.02 0.044
## block:devices:target 0.05 1.21e-05 2.17e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 21.03498 ±0.72%
## [2] block + participant : 0.07502433 ±1.03%
## [3] target + block + participant : 1.643102 ±1.26%
## [4] target + block + target:block + participant : 0.08706431 ±1.35%
## [5] devices + participant : 0.1789219 ±0.73%
## [6] target + devices + participant : 4.199105 ±5.2%
## [7] block + devices + participant : 0.0137383 ±2.17%
## [8] target + block + devices + participant : 0.3056899 ±4.11%
## [9] target + block + target:block + devices + participant : 0.01679315 ±2.61%
## [10] target + devices + target:devices + participant : 0.2869189 ±5.1%
## [11] target + block + devices + target:devices + participant : 0.02281697 ±3.12%
## [12] target + block + target:block + devices + target:devices + participant : 0.001195459 ±2.57%
## [13] block + devices + block:devices + participant : 0.001642812 ±2.27%
## [14] target + block + devices + block:devices + participant : 0.03696966 ±2.25%
## [15] target + block + target:block + devices + block:devices + participant : 0.002064438 ±3.65%
## [16] target + block + devices + target:devices + block:devices + participant : 0.00285258 ±7.14%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.0001441919 ±2.46%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1.357097e-05 ±2.84%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.96 7.78
## block 0.74 0.08 0.030
## block:target 0.32 3.71e-03 0.008
## devices 0.74 0.18 0.076
## devices:target 0.32 0.01 0.024
## block:devices 0.32 1.51e-03 0.003
## block:devices:target 0.05 4.69e-07 8.45e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.07033112 ±0.66%
## [2] block + participant : 0.03563951 ±0.88%
## [3] target + block + participant : 0.002555498 ±1.33%
## [4] target + block + target:block + participant : 3.371219e-05 ±1.07%
## [5] devices + participant : 0.4076237 ±0.85%
## [6] target + devices + participant : 0.02894507 ±1.37%
## [7] block + devices + participant : 0.01457107 ±1.23%
## [8] target + block + devices + participant : 0.001051545 ±2.14%
## [9] target + block + target:block + devices + participant : 1.539198e-05 ±5.81%
## [10] target + devices + target:devices + participant : 0.1045416 ±1.54%
## [11] target + block + devices + target:devices + participant : 0.003700898 ±1.51%
## [12] target + block + target:block + devices + target:devices + participant : 5.161408e-05 ±1.83%
## [13] block + devices + block:devices + participant : 0.001558466 ±2.4%
## [14] target + block + devices + block:devices + participant : 0.0001024104 ±1.53%
## [15] target + block + target:block + devices + block:devices + participant : 1.443189e-06 ±4.38%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0003776303 ±2.24%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 5.536666e-06 ±2.83%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 3.064896e-07 ±8.42%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.13 0.052
## block 0.74 0.04 0.013
## block:target 0.32 6.46e-05 1.40e-04
## devices 0.74 0.34 0.181
## devices:target 0.32 0.07 0.151
## block:devices 0.32 1.22e-03 0.003
## block:devices:target 0.05 1.83e-07 3.30e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.298263 ±1.18%
## [2] block + participant : 0.1068223 ±0.56%
## [3] target + block + participant : 0.03261679 ±1.18%
## [4] target + block + target:block + participant : 0.001154823 ±1.71%
## [5] devices + participant : 0.2088153 ±0.87%
## [6] target + devices + participant : 0.06219272 ±1.19%
## [7] block + devices + participant : 0.0235241 ±1.38%
## [8] target + block + devices + participant : 0.008240287 ±11.01%
## [9] target + block + target:block + devices + participant : 0.0002536637 ±1.85%
## [10] target + devices + target:devices + participant : 0.02104686 ±1.65%
## [11] target + block + devices + target:devices + participant : 0.002856415 ±13.13%
## [12] target + block + target:block + devices + target:devices + participant : 8.868426e-05 ±3.42%
## [13] block + devices + block:devices + participant : 0.002756023 ±5.17%
## [14] target + block + devices + block:devices + participant : 0.0008099991 ±3.39%
## [15] target + block + target:block + devices + block:devices + participant : 2.796618e-05 ±1.88%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0002836959 ±4.16%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.000489e-05 ±3.63%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 7.701098e-07 ±4.12%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.24 0.114
## block 0.74 0.10 0.040
## block:target 0.32 8.68e-04 0.002
## devices 0.74 0.19 0.082
## devices:target 0.32 0.01 0.030
## block:devices 0.32 2.20e-03 0.005
## block:devices:target 0.05 4.35e-07 7.83e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.03078111 ±7.04%
## [2] block + participant : 0.08822376 ±0.79%
## [3] target + block + participant : 0.002487561 ±1.08%
## [4] target + block + target:block + participant : 9.875396e-05 ±1.76%
## [5] devices + participant : 0.209819 ±1.02%
## [6] target + devices + participant : 0.005817741 ±1.3%
## [7] block + devices + participant : 0.0179289 ±1.02%
## [8] target + block + devices + participant : 0.0005263314 ±2.11%
## [9] target + block + target:block + devices + participant : 2.13898e-05 ±4.49%
## [10] target + devices + target:devices + participant : 0.000494898 ±2.67%
## [11] target + block + devices + target:devices + participant : 4.209967e-05 ±2.35%
## [12] target + block + target:block + devices + target:devices + participant : 1.939197e-06 ±8.65%
## [13] block + devices + block:devices + participant : 0.004842965 ±1.6%
## [14] target + block + devices + block:devices + participant : 0.0001405133 ±2.07%
## [15] target + block + target:block + devices + block:devices + participant : 5.413534e-06 ±2.05%
## [16] target + block + devices + target:devices + block:devices + participant : 1.104207e-05 ±2.79%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 5.134246e-07 ±9.33%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 8.345584e-08 ±5.13%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.011
## block 0.74 0.08 0.033
## block:target 0.32 9.41e-05 2.04e-04
## devices 0.74 0.18 0.076
## devices:target 0.32 4.04e-04 8.77e-04
## block:devices 0.32 3.67e-03 0.008
## block:devices:target 0.05 6.13e-08 1.10e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target x block x device interaction in quadrant 1, and a significant device x target interaction in quadrant 2. However, both interactions did not hold up in the Bayesian tests.
deviceLearningGenQ1ComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## 1st block, Far: Mouse vs. Trackpad -2.13 17.6 46 -0.121 1.0000
## 1st block, Mid: Mouse vs. Trackpad 4.17 31.2 46 0.134 1.0000
## 1st block, Near: Mouse vs. Trackpad 217.46 170.6 46 1.275 1.0000
## 2nd block, Far: Mouse vs. Trackpad -5.85 13.2 46 -0.442 1.0000
## 2nd block, Mid: Mouse vs. Trackpad 15.18 23.2 46 0.655 1.0000
## 2nd block, Near: Mouse vs. Trackpad -86.39 168.8 46 -0.512 1.0000
## Last block, Far: Mouse vs. Trackpad -15.65 12.0 46 -1.303 1.0000
## Last block, Mid: Mouse vs. Trackpad -22.01 24.3 46 -0.907 1.0000
## Last block, Near: Mouse vs. Trackpad -474.19 186.0 46 -2.550 0.1275
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block, Far: Mouse vs. Trackpad 0.0003175400
## 2 1st block, Mid: Mouse vs. Trackpad 0.0003892389
## 3 1st block, Near: Mouse vs. Trackpad 0.0341192543
## 4 2nd block, Far: Mouse vs. Trackpad 0.0042369286
## 5 2nd block, Mid: Mouse vs. Trackpad 0.0092533096
## 6 2nd block, Near: Mouse vs. Trackpad 0.0056622865
## 7 Last block, Far: Mouse vs. Trackpad 0.0356188074
## 8 Last block, Mid: Mouse vs. Trackpad 0.0175713290
## 9 Last block, Near: Mouse vs. Trackpad 0.1238458321deviceLearningGenQ1Bayesfollowup()## FIRST BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3494754 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3499077 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6373397 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## SECOND BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3739977 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4081957 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3833817 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## LAST BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6551173 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4727567 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.792378 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests in quadrant 1 show that there are no differences between devices across blocks and targets. However, Bayesian test comparing devices in the near target during the last block show anecdotal evidence for a difference. In the plot, this is seen with how mouse users were over compensating during the last block.
deviceLearningGenQ2ComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## Far: Mouse vs. Trackpad 0.589 12.2 46 0.048 1.0000
## Mid: Mouse vs. Trackpad 18.169 14.1 46 1.290 0.6108
## Near: Mouse vs. Trackpad -183.758 93.1 46 -1.973 0.1637
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far: Mouse vs. Trackpad 5.068625e-05
## 2 Mid: Mouse vs. Trackpad 3.489785e-02
## 3 Near: Mouse vs. Trackpad 7.800233e-02deviceLearningGenQ2Bayesfollowup()## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3478715 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6465031 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.471201 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests for quadrant 2 show no effects. But, Bayesian follow-up test on the near target show anecdotal evidence of a difference between devices. In the plot, this is again observed with how mouse users are overcompensating.
Next, we check washout trials.
deviceWashoutLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.08261926 7.750697e-01 0.0003181499
## 3 block 2 92 10.74151022 6.418289e-05 * 0.0319004449
## 5 target 2 92 3.40464158 3.745792e-02 * 0.0164102681
## 4 devices:block 2 92 0.40185900 6.702438e-01 0.0012312607
## 6 devices:target 2 92 1.71088674 1.864042e-01 0.0083142983
## 7 block:target 4 184 0.75187744 5.579354e-01 0.0074026893
## 8 devices:block:target 4 184 1.36135098 2.490783e-01 0.0133233771
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9058906 0.10819439
## 4 devices:block 0.9058906 0.10819439
## 5 target 0.8548781 0.02936596 *
## 6 devices:target 0.8548781 0.02936596 *
## 7 block:target 0.7824046 0.28302520
## 8 devices:block:target 0.7824046 0.28302520
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9139854 0.0001154594 * 0.9498616 9.036103e-05
## 4 devices:block 0.9139854 0.6518699397 0.9498616 6.597401e-01
## 5 target 0.8732695 0.0442237316 * 0.9048708 4.243060e-02
## 6 devices:target 0.8732695 0.1906819859 0.9048708 1.896600e-01
## 7 block:target 0.8902629 0.5437754668 0.9741608 5.547372e-01
## 8 devices:block:target 0.8902629 0.2529008689 0.9741608 2.500004e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8deviceWashoutLearningBayesANOVA()## Quadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.9582829 ±1.03%
## [2] block + participant : 340.9324 ±1.05%
## [3] target + block + participant : 388.4839 ±1.16%
## [4] target + block + target:block + participant : 21.97576 ±2.22%
## [5] devices + participant : 0.1981215 ±1.09%
## [6] target + devices + participant : 0.1866545 ±2.18%
## [7] block + devices + participant : 67.7382 ±1.02%
## [8] target + block + devices + participant : 82.12294 ±6.11%
## [9] target + block + target:block + devices + participant : 4.590868 ±2.86%
## [10] target + devices + target:devices + participant : 0.05788421 ±2.08%
## [11] target + block + devices + target:devices + participant : 25.90792 ±4.52%
## [12] target + block + target:block + devices + target:devices + participant : 1.4554 ±2.02%
## [13] block + devices + block:devices + participant : 5.713334 ±1.5%
## [14] target + block + devices + block:devices + participant : 6.783922 ±2.15%
## [15] target + block + target:block + devices + block:devices + participant : 0.3842254 ±2.55%
## [16] target + block + devices + target:devices + block:devices + participant : 2.156605 ±2.59%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.1299619 ±3.53%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.04461767 ±3.53%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.56 0.460
## block 0.74 1.00 141.08
## block:target 0.32 0.03 0.067
## devices 0.74 0.21 0.094
## devices:target 0.32 0.03 0.070
## block:devices 0.32 0.02 0.035
## block:devices:target 0.05 4.69e-05 8.45e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any device effects. Thus, it seems that overall learning between mouse and trackpad users are the same, but mouse users tend to overcompensate for the near target.
Completion time
plotDeviceCtrlGenMT()
We conduct the same 3x3x2 mixed design ANOVA with completion time as the dependent variable. We conduct this test for reaches to quadrants 1, 4, 2, top-up quadrant 1 trials, quadrant 1 trials after switching hands, and washout trials.
deviceGenmovementtimeANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.4738681 4.946702e-01 0.0051476802
## 3 block 2 92 19.9637500 6.292377e-08 * 0.0557389520
## 5 target 2 92 14.3206476 3.849678e-06 * 0.0520464110
## 4 devices:block 2 92 0.3684162 6.928452e-01 0.0010881542
## 6 devices:target 2 92 0.1424615 8.674119e-01 0.0005458853
## 7 block:target 4 184 8.4807468 2.658594e-06 * 0.0330407298
## 8 devices:block:target 4 184 2.3003942 6.041924e-02 0.0091833872
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8628752 0.0362101291 *
## 4 devices:block 0.8628752 0.0362101291 *
## 5 target 0.9664270 0.4637711857
## 6 devices:target 0.9664270 0.4637711857
## 7 block:target 0.5085996 0.0004378574 *
## 8 devices:block:target 0.5085996 0.0004378574 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8794110 3.139987e-07 * 0.9116465 2.042336e-07
## 4 devices:block 0.8794110 6.658229e-01 0.9116465 6.734108e-01
## 5 target 0.9675175 5.229155e-06 * 1.0092672 3.849678e-06
## 6 devices:target 0.9675175 8.609116e-01 1.0092672 8.674119e-01
## 7 block:target 0.7487597 3.320726e-05 * 0.8066908 1.851112e-05
## 8 devices:block:target 0.7487597 8.012260e-02 0.8066908 7.505375e-02
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.2343380 6.306226e-01 0.0023688294
## 3 block 2 92 11.2260437 4.340593e-05 * 0.0276790668
## 5 target 2 92 21.1967950 2.684272e-08 * 0.0949135769
## 4 devices:block 2 92 0.1183972 8.884783e-01 0.0003001416
## 6 devices:target 2 92 1.0681142 3.478784e-01 0.0052565027
## 7 block:target 4 184 0.6587037 6.214667e-01 0.0027087588
## 8 devices:block:target 4 184 0.2751536 8.937514e-01 0.0011332898
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9354328 0.2227321744
## 4 devices:block 0.9354328 0.2227321744
## 5 target 0.9412290 0.2559437200
## 6 devices:target 0.9412290 0.2559437200
## 7 block:target 0.4748189 0.0001307358 *
## 8 devices:block:target 0.4748189 0.0001307358 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9393488 6.710403e-05 * 0.9779719 5.084221e-05
## 4 devices:block 0.9393488 8.767739e-01 0.9779719 8.843785e-01
## 5 target 0.9444913 5.882392e-08 * 0.9836792 3.380403e-08
## 6 devices:target 0.9444913 3.450647e-01 0.9836792 3.470785e-01
## 7 block:target 0.7375668 5.763763e-01 0.7936318 5.871447e-01
## 8 devices:block:target 0.7375668 8.400600e-01 0.7936318 8.538308e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.01758916 8.950691e-01 0.0001028463
## 3 block 2 92 9.75135981 1.442477e-04 * 0.0345880069
## 5 target 2 92 10.89412416 5.672299e-05 * 0.0489908880
## 4 devices:block 2 92 3.15140486 4.744683e-02 * 0.0114459615
## 6 devices:target 2 92 4.35016451 1.566099e-02 * 0.0201558445
## 7 block:target 4 184 4.45651295 1.843341e-03 * 0.0322954676
## 8 devices:block:target 4 184 2.90214828 2.321516e-02 * 0.0212708934
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.417868667 2.974375e-09 *
## 4 devices:block 0.417868667 2.974375e-09 *
## 5 target 0.500373408 1.714431e-07 *
## 6 devices:target 0.500373408 1.714431e-07 *
## 7 block:target 0.005201721 4.530811e-45 *
## 8 devices:block:target 0.005201721 4.530811e-45 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6320588 0.0013701739 * 0.6416943 0.0012912284
## 4 devices:block 0.6320588 0.0716403612 0.6416943 0.0708889384
## 5 target 0.6668327 0.0005783151 * 0.6792842 0.0005299791
## 6 devices:target 0.6668327 0.0305516331 * 0.6792842 0.0297984552
## 7 block:target 0.3001083 0.0327102041 * 0.3036880 0.0322271294
## 8 devices:block:target 0.3001083 0.0872423898 0.3036880 0.0866829351
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6 *
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 1.8926464 1.755658e-01 0.0180247392
## 3 block 2 92 2.9212299 5.888184e-02 0.0105538053
## 5 target 2 92 12.7295572 1.316591e-05 * 0.0531244954
## 4 devices:block 2 92 0.2565872 7.742394e-01 0.0009360076
## 6 devices:target 2 92 1.2737331 2.846721e-01 0.0055825909
## 7 block:target 4 184 0.9470745 4.380101e-01 0.0037570464
## 8 devices:block:target 4 184 2.9710145 2.078023e-02 * 0.0116921442
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8183893 0.0110052 *
## 4 devices:block 0.8183893 0.0110052 *
## 5 target 0.9821733 0.6671645
## 6 devices:target 0.9821733 0.6671645
## 7 block:target 0.7750367 0.2547823
## 8 devices:block:target 0.7750367 0.2547823
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8463024 6.831510e-02 0.8751634 6.644188e-02
## 4 devices:block 0.8463024 7.372079e-01 0.8751634 7.447559e-01
## 5 target 0.9824855 1.522072e-05 * 1.0259292 1.316591e-05
## 6 devices:target 0.9824855 2.844400e-01 1.0259292 2.846721e-01
## 7 block:target 0.8883546 4.306803e-01 0.9718725 4.362629e-01
## 8 devices:block:target 0.8883546 2.587862e-02 * 0.9718725 2.195776e-02
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8 *## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.02252572 8.813532e-01 0.0001545233
## 3 block 2 92 4.77795157 1.061212e-02 * 0.0197046957
## 5 target 2 92 13.98615860 4.971780e-06 * 0.0519638080
## 4 devices:block 2 92 0.89423697 4.124435e-01 0.0037479425
## 6 devices:target 2 92 3.43404440 3.644665e-02 * 0.0132793774
## 7 block:target 4 184 2.29623624 6.081431e-02 0.0152679329
## 8 devices:block:target 4 184 1.32767623 2.612832e-01 0.0088850891
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8400869 1.982873e-02 *
## 4 devices:block 0.8400869 1.982873e-02 *
## 5 target 0.7591667 2.030422e-03 *
## 6 devices:target 0.7591667 2.030422e-03 *
## 7 block:target 0.1709430 3.480640e-13 *
## 8 devices:block:target 0.1709430 3.480640e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8621336 1.461884e-02 * 0.8925945 1.361842e-02
## 4 devices:block 0.8621336 3.995833e-01 0.8925945 4.026251e-01
## 5 target 0.8059100 2.970727e-05 * 0.8308016 2.360736e-05
## 6 devices:target 0.8059100 4.718759e-02 * 0.8308016 4.565253e-02
## 7 block:target 0.5062146 1.056520e-01 0.5296648 1.029493e-01
## 8 devices:block:target 0.5062146 2.701794e-01 0.5296648 2.703196e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6 *
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.09223208 7.627279e-01 0.0007944006
## 3 block 2 92 48.46373213 4.213720e-15 * 0.0937031397
## 5 target 2 92 3.15511683 4.728230e-02 * 0.0117658444
## 4 devices:block 2 92 0.34028035 7.124626e-01 0.0007254183
## 6 devices:target 2 92 0.52692747 5.921873e-01 0.0019844308
## 7 block:target 4 184 2.41755540 5.025228e-02 0.0171373687
## 8 devices:block:target 4 184 0.30007200 8.776257e-01 0.0021595410
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8808858 5.763567e-02
## 4 devices:block 0.8808858 5.763567e-02
## 5 target 0.7375330 1.059456e-03 *
## 6 devices:target 0.7375330 1.059456e-03 *
## 7 block:target 0.1113585 5.550718e-17 *
## 8 devices:block:target 0.1113585 5.550718e-17 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8935639 9.579026e-14 * 0.9272752 3.559950e-14
## 4 devices:block 0.8935639 6.883389e-01 0.9272752 6.963034e-01
## 5 target 0.7920999 5.980682e-02 0.8156714 5.824123e-02
## 6 devices:target 0.7920999 5.511118e-01 0.8156714 5.562547e-01
## 7 block:target 0.5075606 9.388441e-02 0.5311684 9.112656e-02
## 8 devices:block:target 0.5075606 7.447361e-01 0.5311684 7.545234e-01
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8deviceGenmovementtimeBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 367786479 ±0.62%
## [2] block + participant : 700978988 ±2.04%
## [3] target + block + participant : 8.186453e+18 ±1.94%
## [4] target + block + target:block + participant : 3.657649e+20 ±1.35%
## [5] devices + participant : 0.3578305 ±0.81%
## [6] target + devices + participant : 138846481 ±1.38%
## [7] block + devices + participant : 255973847 ±1.27%
## [8] target + block + devices + participant : 3.206137e+18 ±1.58%
## [9] target + block + target:block + devices + participant : 1.45104e+20 ±2.33%
## [10] target + devices + target:devices + participant : 11562497 ±2.35%
## [11] target + block + devices + target:devices + participant : 2.596366e+17 ±1.72%
## [12] target + block + target:block + devices + target:devices + participant : 1.292793e+19 ±3.9%
## [13] block + devices + block:devices + participant : 22885223 ±1.68%
## [14] target + block + devices + block:devices + participant : 2.991685e+17 ±2.6%
## [15] target + block + target:block + devices + block:devices + participant : 1.315425e+19 ±7.92%
## [16] target + block + devices + target:devices + block:devices + participant : 2.736437e+16 ±12.45%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.29223e+18 ±7.26%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 2.641895e+17 ±2.06%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.01e+11
## block 0.74 1.00 3.79e+11
## block:target 0.32 0.98 97.40
## devices 0.74 0.32 0.169
## devices:target 0.32 0.03 0.060
## block:devices 0.32 0.03 0.061
## block:devices:target 0.05 4.80e-04 0.009
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 4.919814e+14 ±2.47%
## [2] block + participant : 1083.024 ±2.87%
## [3] target + block + participant : 5.943601e+18 ±1.55%
## [4] target + block + target:block + participant : 2.438196e+17 ±1.21%
## [5] devices + participant : 0.3224707 ±1.96%
## [6] target + devices + participant : 1.642422e+14 ±1.29%
## [7] block + devices + participant : 336.5494 ±1.49%
## [8] target + block + devices + participant : 2.072669e+18 ±1.54%
## [9] target + block + target:block + devices + participant : 8.607317e+16 ±1.55%
## [10] target + devices + target:devices + participant : 4.020406e+13 ±1.38%
## [11] target + block + devices + target:devices + participant : 5.609273e+17 ±2.47%
## [12] target + block + target:block + devices + target:devices + participant : 2.338436e+16 ±2.08%
## [13] block + devices + block:devices + participant : 26.63828 ±6.65%
## [14] target + block + devices + block:devices + participant : 1.493843e+17 ±1.62%
## [15] target + block + target:block + devices + block:devices + participant : 6.398587e+15 ±1.78%
## [16] target + block + devices + target:devices + block:devices + participant : 4.264172e+16 ±4.67%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.841019e+15 ±2.99%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1.125885e+14 ±2.46%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.25e+15
## block 0.74 1.00 4.68e+03
## block:target 0.32 0.04 0.089
## devices 0.74 0.32 0.170
## devices:target 0.32 0.07 0.160
## block:devices 0.32 0.02 0.049
## block:devices:target 0.05 1.23e-05 2.22e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 371.176 ±3.12%
## [2] block + participant : 5.16506 ±2.96%
## [3] target + block + participant : 2438.427 ±2.6%
## [4] target + block + target:block + participant : 389.6101 ±6.45%
## [5] devices + participant : 0.2181858 ±0.89%
## [6] target + devices + participant : 78.61076 ±1.16%
## [7] block + devices + participant : 1.134437 ±1.89%
## [8] target + block + devices + participant : 547.4337 ±1.97%
## [9] target + block + target:block + devices + participant : 86.2125 ±4.93%
## [10] target + devices + target:devices + participant : 279.8678 ±5.21%
## [11] target + block + devices + target:devices + participant : 2196.421 ±5.28%
## [12] target + block + target:block + devices + target:devices + participant : 341.0133 ±4.74%
## [13] block + devices + block:devices + participant : 0.5592592 ±1.92%
## [14] target + block + devices + block:devices + participant : 295.9774 ±2.03%
## [15] target + block + target:block + devices + block:devices + participant : 51.53425 ±4.69%
## [16] target + block + devices + target:devices + block:devices + participant : 1128.885 ±2.62%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 211.8388 ±5.74%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 128.8986 ±2.35%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 377.88
## block 0.74 0.91 3.82
## block:target 0.32 0.14 0.357
## devices 0.74 0.63 0.596
## devices:target 0.32 0.50 2.18
## block:devices 0.32 0.21 0.585
## block:devices:target 0.05 0.02 0.275
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 17811381391 ±1.27%
## [2] block + participant : 0.5618247 ±0.75%
## [3] target + block + participant : 16277584968 ±1.14%
## [4] target + block + target:block + participant : 439882857 ±1.56%
## [5] devices + participant : 0.6245473 ±2.23%
## [6] target + devices + participant : 11306238271 ±2.02%
## [7] block + devices + participant : 0.3422901 ±2.39%
## [8] target + block + devices + participant : 10344205478 ±2.27%
## [9] target + block + target:block + devices + participant : 286528966 ±3.76%
## [10] target + devices + target:devices + participant : 3920908316 ±1.38%
## [11] target + block + devices + target:devices + participant : 3620967341 ±1.45%
## [12] target + block + target:block + devices + target:devices + participant : 98451140 ±1.9%
## [13] block + devices + block:devices + participant : 0.0286603 ±1.83%
## [14] target + block + devices + block:devices + participant : 862226793 ±1.62%
## [15] target + block + target:block + devices + block:devices + participant : 24260039 ±4.55%
## [16] target + block + devices + target:devices + block:devices + participant : 337860890 ±3.75%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 8272597 ±2.24%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 4850260 ±2.23%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 9.13e+09
## block 0.74 0.49 0.349
## block:target 0.32 0.01 0.029
## devices 0.74 0.47 0.319
## devices:target 0.32 0.12 0.302
## block:devices 0.32 0.02 0.042
## block:devices:target 0.05 7.42e-05 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 38495.9 ±0.9%
## [2] block + participant : 85.28568 ±0.95%
## [3] target + block + participant : 6211529 ±2.85%
## [4] target + block + target:block + participant : 4477843 ±20.79%
## [5] devices + participant : 0.2348434 ±0.85%
## [6] target + devices + participant : 9303.367 ±1.81%
## [7] block + devices + participant : 20.10991 ±1.2%
## [8] target + block + devices + participant : 1480936 ±1.52%
## [9] target + block + target:block + devices + participant : 916048.7 ±8.63%
## [10] target + devices + target:devices + participant : 9769.809 ±1.47%
## [11] target + block + devices + target:devices + participant : 1789343 ±1.91%
## [12] target + block + target:block + devices + target:devices + participant : 1116973 ±1.62%
## [13] block + devices + block:devices + participant : 3.283583 ±2.76%
## [14] target + block + devices + block:devices + participant : 299281.8 ±16.57%
## [15] target + block + target:block + devices + block:devices + participant : 158281.3 ±2.34%
## [16] target + block + devices + target:devices + block:devices + participant : 329150.8 ±4.83%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 194761 ±2.22%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 41855.87 ±2.24%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.55e+04
## block 0.74 1.00 105.56
## block:target 0.32 0.40 1.47
## devices 0.74 0.37 0.211
## devices:target 0.32 0.20 0.555
## block:devices 0.32 0.06 0.138
## block:devices:target 0.05 2.45e-03 0.044
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 3.94576 ±0.91%
## [2] block + participant : 1.984303e+17 ±0.72%
## [3] target + block + participant : 2.939489e+18 ±1.29%
## [4] target + block + target:block + participant : 2.578144e+20 ±2.3%
## [5] devices + participant : 0.2602821 ±0.71%
## [6] target + devices + participant : 1.030517 ±1.15%
## [7] block + devices + participant : 5.752933e+16 ±1.3%
## [8] target + block + devices + participant : 9.093144e+17 ±6.66%
## [9] target + block + target:block + devices + participant : 7.795362e+19 ±4.56%
## [10] target + devices + target:devices + participant : 0.1201003 ±2.88%
## [11] target + block + devices + target:devices + participant : 1.047649e+17 ±1.46%
## [12] target + block + target:block + devices + target:devices + participant : 9.254647e+18 ±1.91%
## [13] block + devices + block:devices + participant : 5.322776e+15 ±1.71%
## [14] target + block + devices + block:devices + participant : 7.871715e+16 ±2.15%
## [15] target + block + target:block + devices + block:devices + participant : 8.34083e+18 ±17.45%
## [16] target + block + devices + target:devices + block:devices + participant : 9.638344e+15 ±2.56%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 8.540466e+17 ±2.27%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 9.067725e+16 ±3.26%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 489.82
## block 0.74 1.00 2.01e+19
## block:target 0.32 0.99 178.39
## devices 0.74 0.27 0.134
## devices:target 0.32 0.03 0.064
## block:devices 0.32 0.03 0.058
## block:devices:target 0.05 2.53e-04 0.005
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a device x target interaction for quadrants 2 and quadrant 1 after switching hands (1L). We also find a target x block x device interaction for quadrant 1 top-up trials (1A).
deviceMTGenQ2ComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## Far: Mouse vs. Trackpad 0.281 0.217 46 1.298 0.6027
## Mid: Mouse vs. Trackpad -0.810 0.645 46 -1.257 0.6448
## Near: Mouse vs. Trackpad 0.662 0.372 46 1.780 0.2449
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far: Mouse vs. Trackpad 0.03530894
## 2 Mid: Mouse vs. Trackpad 0.03323124
## 3 Near: Mouse vs. Trackpad 0.06446458deviceMTGenQ2Bayesfollowup()## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6513996 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6270623 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.128575 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSQuadrant 2 follow-up tests only show anecdotal evidence of a device effect for the near target.
deviceMTGenQ1LComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## Far: Mouse vs. Trackpad 0.0858 0.314 46 0.273 1.0000
## Mid: Mouse vs. Trackpad -0.6877 0.525 46 -1.309 0.5910
## Near: Mouse vs. Trackpad 0.4494 0.407 46 1.104 0.8263
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far: Mouse vs. Trackpad 0.001621018
## 2 Mid: Mouse vs. Trackpad 0.035919494
## 3 Near: Mouse vs. Trackpad 0.025801706deviceMTGenQ1LBayesfollowup()## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.357428 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6587471 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5478735 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests for Quadrant 1 after switching hands did not reveal any device effects.
deviceMTGenQ1AComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## 1st block, Far: Mouse vs. Trackpad 0.172 0.211 46 0.816 1.0000
## 1st block, Mid: Mouse vs. Trackpad 0.211 0.380 46 0.554 1.0000
## 1st block, Near: Mouse vs. Trackpad 0.284 0.400 46 0.711 1.0000
## 2nd block, Far: Mouse vs. Trackpad 0.311 0.165 46 1.882 0.5960
## 2nd block, Mid: Mouse vs. Trackpad -0.320 0.357 46 -0.894 1.0000
## 2nd block, Near: Mouse vs. Trackpad 0.902 0.413 46 2.182 0.3080
## Last block, Far: Mouse vs. Trackpad 0.249 0.175 46 1.424 1.0000
## Last block, Mid: Mouse vs. Trackpad 0.511 0.392 46 1.303 1.0000
## Last block, Near: Mouse vs. Trackpad 0.410 0.350 46 1.172 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block, Far: Mouse vs. Trackpad 0.014266646
## 2 1st block, Mid: Mouse vs. Trackpad 0.006632486
## 3 1st block, Near: Mouse vs. Trackpad 0.010878875
## 4 2nd block, Far: Mouse vs. Trackpad 0.071467462
## 5 2nd block, Mid: Mouse vs. Trackpad 0.017092179
## 6 2nd block, Near: Mouse vs. Trackpad 0.093821590
## 7 Last block, Far: Mouse vs. Trackpad 0.042234612
## 8 Last block, Mid: Mouse vs. Trackpad 0.035597195
## 9 Last block, Near: Mouse vs. Trackpad 0.028982434deviceMTGenQ1ABayesfollowup()## FIRST BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4458497 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3899175 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4200063 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## SECOND BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.29343 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4687469 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.022082 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## LAST BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7403178 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6548573 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5803437 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests on quadrant 1 top-up trials only show anecdotal evidence of a device effect for the far target in the second block, and the near target in the second block. In both cases, we see in the plot that these are when mouse users were moving a bit faster than trackpad users. Thus, there is only a small amount of evidence showing that mouse users initiate and execute movements faster than trackpad users.
Path length
plotDeviceCtrlGenPL()
We repeat the same tests and have path length as the dependent variable.
deviceGenpathlengthANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.005693493 9.401797e-01 3.601462e-05
## 3 block 2 92 24.465833424 3.018874e-09 * 7.278182e-02
## 5 target 2 92 12.603567382 1.453295e-05 * 4.995583e-02
## 4 devices:block 2 92 2.431198222 9.356220e-02 7.739750e-03
## 6 devices:target 2 92 0.091238382 9.128826e-01 3.805057e-04
## 7 block:target 4 184 5.469689437 3.495183e-04 * 4.208841e-02
## 8 devices:block:target 4 184 0.931441335 4.468902e-01 7.426644e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9828341 6.773370e-01
## 4 devices:block 0.9828341 6.773370e-01
## 5 target 0.9156023 1.375322e-01
## 6 devices:target 0.9156023 1.375322e-01
## 7 block:target 0.3488107 4.412479e-07 *
## 8 devices:block:target 0.3488107 4.412479e-07 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9831238 3.969633e-09 * 1.0266401 3.018874e-09
## 4 devices:block 0.9831238 9.457449e-02 1.0266401 9.356220e-02
## 5 target 0.9221709 2.750289e-05 * 0.9589265 2.034572e-05
## 6 devices:target 0.9221709 8.990852e-01 0.9589265 9.058794e-01
## 7 block:target 0.6956489 1.890690e-03 * 0.7449660 1.435291e-03
## 8 devices:block:target 0.6956489 4.221016e-01 0.7449660 4.269312e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.04717119 8.290213e-01 0.0003308386
## 3 block 2 92 6.22659739 2.909649e-03 * 0.0209652026
## 5 target 2 92 25.52178196 1.522991e-09 * 0.1098435096
## 4 devices:block 2 92 0.92806668 3.989861e-01 0.0031815985
## 6 devices:target 2 92 1.12403244 3.293880e-01 0.0054053276
## 7 block:target 4 184 1.76514612 1.377001e-01 0.0112554566
## 8 devices:block:target 4 184 0.88329227 4.750538e-01 0.0056641647
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9474348 2.967292e-01
## 4 devices:block 0.9474348 2.967292e-01
## 5 target 0.9080946 1.142746e-01
## 6 devices:target 0.9080946 1.142746e-01
## 7 block:target 0.4051923 7.335101e-06 *
## 8 devices:block:target 0.4051923 7.335101e-06 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9500599 3.450673e-03 * 0.9898625 3.012060e-03
## 4 devices:block 0.9500599 3.949751e-01 0.9898625 3.981923e-01
## 5 target 0.9158303 6.312068e-09 * 0.9519041 3.430971e-09
## 6 devices:target 0.9158303 3.259253e-01 0.9519041 3.274821e-01
## 7 block:target 0.6860138 1.618634e-01 0.7338333 1.580032e-01
## 8 devices:block:target 0.6860138 4.440754e-01 0.7338333 4.497096e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.1096892 0.7420023849 0.0009098027
## 3 block 2 92 3.3118029 0.0408431980 * 0.0112149278
## 5 target 2 92 8.1976286 0.0005293796 * 0.0355530095
## 4 devices:block 2 92 1.3845076 0.2556154836 0.0047192290
## 6 devices:target 2 92 0.5911812 0.5557622971 0.0026514130
## 7 block:target 4 184 0.6084793 0.6570231867 0.0033448910
## 8 devices:block:target 4 184 0.8368743 0.5033486187 0.0045946395
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9628809 0.42695617
## 4 devices:block 0.9628809 0.42695617
## 5 target 0.9264571 0.17929550
## 6 devices:target 0.9264571 0.17929550
## 7 block:target 0.6311062 0.01543016 *
## 8 devices:block:target 0.6311062 0.01543016 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9642095 0.0427028303 * 1.0055878 0.0408431980
## 4 devices:block 0.9642095 0.2556824719 1.0055878 0.2556154836
## 5 target 0.9314951 0.0007412512 * 0.9692608 0.0006156366
## 6 devices:target 0.9314951 0.5443419422 0.9692608 0.5507329368
## 7 block:target 0.8282292 0.6265220392 0.9001967 0.6399694667
## 8 devices:block:target 0.8282292 0.4853422939 0.9001967 0.4933095630
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.2928023 0.5910413717 0.0028057463
## 3 block 2 92 4.4973195 0.0136935886 * 0.0166229409
## 5 target 2 92 9.2128940 0.0002254222 * 0.0372658269
## 4 devices:block 2 92 0.1346445 0.8741984485 0.0005058282
## 6 devices:target 2 92 1.0570407 0.3516641440 0.0044215599
## 7 block:target 4 184 2.3423662 0.0565673989 0.0096721962
## 8 devices:block:target 4 184 2.1882015 0.0719961221 0.0090413686
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8477415 0.02431801 *
## 4 devices:block 0.8477415 0.02431801 *
## 5 target 0.8552974 0.02969173 *
## 6 devices:target 0.8552974 0.02969173 *
## 7 block:target 0.7596980 0.20218717
## 8 devices:block:target 0.7596980 0.20218717
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8678608 0.0181041181 * 0.8989068 0.016953064
## 4 devices:block 0.8678608 0.8457718394 0.8989068 0.853065219
## 5 target 0.8735893 0.0004625928 * 0.9052236 0.000386314
## 6 devices:target 0.8735893 0.3445492303 0.9052236 0.346477549
## 7 block:target 0.8695411 0.0659008193 0.9493577 0.060013913
## 8 devices:block:target 0.8695411 0.0818963668 0.9493577 0.075681179
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 3.7835062 0.0578873022 0.026442801
## 3 block 2 92 7.6909283 0.0008154893 * 0.021929049
## 5 target 2 92 9.5678918 0.0001678649 * 0.045056405
## 4 devices:block 2 92 0.1289765 0.8791532754 0.000375853
## 6 devices:target 2 92 0.3124067 0.7324569726 0.001538206
## 7 block:target 4 184 3.6377960 0.0070444378 * 0.023841177
## 8 devices:block:target 4 184 1.7285560 0.1454777373 0.011472057
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8508093 0.026376967 *
## 4 devices:block 0.8508093 0.026376967 *
## 5 target 0.8840277 0.062442697
## 6 devices:target 0.8840277 0.062442697
## 7 block:target 0.5527257 0.001814325 *
## 8 devices:block:target 0.5527257 0.001814325 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8701776 0.0014692332 * 0.9014611 0.001274583
## 4 devices:block 0.8701776 0.8516358612 0.9014611 0.858872175
## 5 target 0.8960796 0.0003115777 * 0.9300554 0.000254474
## 6 devices:target 0.8960796 0.7085849757 0.9300554 0.716719040
## 7 block:target 0.7612404 0.0140193028 * 0.8212843 0.011778746
## 8 devices:block:target 0.7612404 0.1631252481 0.8212843 0.158542492
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 1.300527 2.600199e-01 0.005827370
## 3 block 2 92 33.819146 9.770904e-12 * 0.123246072
## 5 target 2 92 7.646321 8.472717e-04 * 0.033297974
## 4 devices:block 2 92 1.395029 2.530183e-01 0.005765074
## 6 devices:target 2 92 1.174315 3.136192e-01 0.005262180
## 7 block:target 4 184 4.934610 8.408801e-04 * 0.040577281
## 8 devices:block:target 4 184 1.209408 3.083371e-01 0.010259218
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.24107814 1.254732e-14 *
## 4 devices:block 0.24107814 1.254732e-14 *
## 5 target 0.71427890 5.152595e-04 *
## 6 devices:target 0.71427890 5.152595e-04 *
## 7 block:target 0.05407965 1.702091e-23 *
## 8 devices:block:target 0.05407965 1.702091e-23 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.5685301 1.213412e-07 * 0.5733221 1.092250e-07
## 4 devices:block 0.5685301 2.471466e-01 0.5733221 2.473498e-01
## 5 target 0.7777737 2.307583e-03 * 0.7999955 2.086804e-03
## 6 devices:target 0.7777737 3.050967e-01 0.7999955 3.061784e-01
## 7 block:target 0.5412987 7.534059e-03 * 0.5689780 6.587372e-03
## 8 devices:block:target 0.5412987 3.047518e-01 0.5689780 3.056659e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8deviceGenpathlengthBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 183814.1 ±0.99%
## [2] block + participant : 3069859 ±1.66%
## [3] target + block + participant : 3.336424e+12 ±10.41%
## [4] target + block + target:block + participant : 6.865158e+14 ±2.49%
## [5] devices + participant : 0.2166814 ±0.97%
## [6] target + devices + participant : 39775.2 ±1.18%
## [7] block + devices + participant : 703133.7 ±2.35%
## [8] target + block + devices + participant : 675812074408 ±1.42%
## [9] target + block + target:block + devices + participant : 1.704121e+14 ±4.01%
## [10] target + devices + target:devices + participant : 3085.68 ±1.99%
## [11] target + block + devices + target:devices + participant : 51455616119 ±2.88%
## [12] target + block + target:block + devices + target:devices + participant : 1.22942e+13 ±4.36%
## [13] block + devices + block:devices + participant : 171791 ±1.53%
## [14] target + block + devices + block:devices + participant : 192894246314 ±1.63%
## [15] target + block + target:block + devices + block:devices + participant : 5.005443e+13 ±3.35%
## [16] target + block + devices + target:devices + block:devices + participant : 16803576100 ±8.09%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3.725565e+12 ±3.89%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 477895688798 ±7.04%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 8.40e+07
## block 0.74 1.00 1.46e+09
## block:target 0.32 1.00 468.22
## devices 0.74 0.26 0.123
## devices:target 0.32 0.02 0.039
## block:devices 0.32 0.06 0.135
## block:devices:target 0.05 5.15e-04 0.009
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 5.285611e+13 ±1.53%
## [2] block + participant : 1.945282 ±0.82%
## [3] target + block + participant : 2.423461e+14 ±1.4%
## [4] target + block + target:block + participant : 7.190008e+13 ±1.24%
## [5] devices + participant : 0.2346934 ±1.36%
## [6] target + devices + participant : 1.325399e+13 ±1.94%
## [7] block + devices + participant : 0.4750692 ±2.5%
## [8] target + block + devices + participant : 6.112429e+13 ±2.42%
## [9] target + block + target:block + devices + participant : 1.868042e+13 ±1.78%
## [10] target + devices + target:devices + participant : 2.395988e+12 ±1.34%
## [11] target + block + devices + target:devices + participant : 1.190882e+13 ±1.91%
## [12] target + block + target:block + devices + target:devices + participant : 3.742353e+12 ±2.85%
## [13] block + devices + block:devices + participant : 0.05282633 ±1.75%
## [14] target + block + devices + block:devices + participant : 7.630394e+12 ±1.78%
## [15] target + block + target:block + devices + block:devices + participant : 2.317436e+12 ±1.8%
## [16] target + block + devices + target:devices + block:devices + participant : 1.607009e+12 ±5.25%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 509251556908 ±8.56%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 58955148565 ±2.33%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 4.72e+13
## block 0.74 0.86 2.20
## block:target 0.32 0.20 0.536
## devices 0.74 0.25 0.120
## devices:target 0.32 0.04 0.093
## block:devices 0.32 0.02 0.055
## block:devices:target 0.05 1.20e-04 0.002
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 2570.92 ±1.31%
## [2] block + participant : 0.1560772 ±0.63%
## [3] target + block + participant : 457.3303 ±1.43%
## [4] target + block + target:block + participant : 7.645377 ±1.59%
## [5] devices + participant : 0.286121 ±1.36%
## [6] target + devices + participant : 759.0724 ±2.82%
## [7] block + devices + participant : 0.04537026 ±1.71%
## [8] target + block + devices + participant : 130.3926 ±1.33%
## [9] target + block + target:block + devices + participant : 2.258504 ±2.24%
## [10] target + devices + target:devices + participant : 88.83503 ±2.52%
## [11] target + block + devices + target:devices + participant : 15.98433 ±3.21%
## [12] target + block + target:block + devices + target:devices + participant : 0.2595457 ±4.35%
## [13] block + devices + block:devices + participant : 0.008405628 ±1.57%
## [14] target + block + devices + block:devices + participant : 26.58433 ±3.65%
## [15] target + block + target:block + devices + block:devices + participant : 0.4364087 ±2.36%
## [16] target + block + devices + target:devices + block:devices + participant : 2.981462 ±1.99%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.05112999 ±2.26%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.005337723 ±3.31%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 969.93
## block 0.74 0.16 0.067
## block:target 0.32 2.62e-03 0.006
## devices 0.74 0.25 0.121
## devices:target 0.32 0.03 0.059
## block:devices 0.32 7.40e-03 0.016
## block:devices:target 0.05 1.31e-06 2.36e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 28156.91 ±0.63%
## [2] block + participant : 12.20618 ±0.73%
## [3] target + block + participant : 554134 ±1.11%
## [4] target + block + target:block + participant : 165150.8 ±0.99%
## [5] devices + participant : 0.3266183 ±0.96%
## [6] target + devices + participant : 9678.551 ±1.48%
## [7] block + devices + participant : 4.024703 ±1.3%
## [8] target + block + devices + participant : 206546.1 ±6.98%
## [9] target + block + target:block + devices + participant : 60207.13 ±4.19%
## [10] target + devices + target:devices + participant : 2089.878 ±4.96%
## [11] target + block + devices + target:devices + participant : 40196.22 ±1.91%
## [12] target + block + target:block + devices + target:devices + participant : 12602.51 ±1.92%
## [13] block + devices + block:devices + participant : 0.3091517 ±1.61%
## [14] target + block + devices + block:devices + participant : 14728.45 ±1.75%
## [15] target + block + target:block + devices + block:devices + participant : 4366.658 ±2.37%
## [16] target + block + devices + target:devices + block:devices + participant : 3106.393 ±2.07%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 895.8609 ±1.74%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 305.3805 ±2.17%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.20e+04
## block 0.74 0.96 9.50
## block:target 0.32 0.22 0.615
## devices 0.74 0.32 0.169
## devices:target 0.32 0.05 0.123
## block:devices 0.32 0.02 0.047
## block:devices:target 0.05 2.77e-04 0.005
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 48941.52 ±0.96%
## [2] block + participant : 73.81227 ±0.77%
## [3] target + block + participant : 6806002 ±1.19%
## [4] target + block + target:block + participant : 6164338 ±1.28%
## [5] devices + participant : 1.088868 ±1.08%
## [6] target + devices + participant : 56247.85 ±2.73%
## [7] block + devices + participant : 78.91834 ±0.95%
## [8] target + block + devices + participant : 7587188 ±1.23%
## [9] target + block + target:block + devices + participant : 7307865 ±3.22%
## [10] target + devices + target:devices + participant : 4905.145 ±2.43%
## [11] target + block + devices + target:devices + participant : 694993.6 ±1.88%
## [12] target + block + target:block + devices + target:devices + participant : 660850.9 ±5.55%
## [13] block + devices + block:devices + participant : 6.282343 ±2.42%
## [14] target + block + devices + block:devices + participant : 663419.5 ±7.04%
## [15] target + block + target:block + devices + block:devices + participant : 531717 ±1.92%
## [16] target + block + devices + target:devices + block:devices + participant : 54272.19 ±3.39%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 49349.57 ±2.63%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 13237.47 ±5.84%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 6.79e+04
## block 0.74 1.00 99.05
## block:target 0.32 0.48 2.00
## devices 0.74 0.58 0.483
## devices:target 0.32 0.05 0.110
## block:devices 0.32 0.04 0.097
## block:devices:target 0.05 4.32e-04 0.008
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 8.05941 ±1.67%
## [2] block + participant : 2.087913e+13 ±1.21%
## [3] target + block + participant : 5.224659e+14 ±3.33%
## [4] target + block + target:block + participant : 3.41933e+15 ±1.18%
## [5] devices + participant : 0.311996 ±3.08%
## [6] target + devices + participant : 2.47746 ±1.49%
## [7] block + devices + participant : 6.821496e+12 ±1.52%
## [8] target + block + devices + participant : 1.672458e+14 ±2.31%
## [9] target + block + target:block + devices + participant : 1.166419e+15 ±3.29%
## [10] target + devices + target:devices + participant : 0.3387779 ±2.03%
## [11] target + block + devices + target:devices + participant : 2.659152e+13 ±4.79%
## [12] target + block + target:block + devices + target:devices + participant : 1.881079e+14 ±1.89%
## [13] block + devices + block:devices + participant : 1.149075e+12 ±1.77%
## [14] target + block + devices + block:devices + participant : 6.774408e+13 ±57.37%
## [15] target + block + target:block + devices + block:devices + participant : 2.084977e+14 ±2.25%
## [16] target + block + devices + target:devices + block:devices + participant : 4.86542e+12 ±3.26%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3.511161e+13 ±2.57%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 4.710416e+12 ±3.21%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 71.94
## block 0.74 1.00 1.71e+14
## block:target 0.32 0.86 13.31
## devices 0.74 0.32 0.169
## devices:target 0.32 0.04 0.101
## block:devices 0.32 0.06 0.126
## block:devices:target 0.05 8.07e-04 0.015
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any device effects for path length in reaches to all quadrants.
Sex: Males vs. females
In session 2 the sample for males (N = 11) was smaller than the sample for females (N = 36). One participant identified as neither and was excluded from the comparisons below.
Learning
plotSexCtrlGen()
We conduct the same 3x3x2 mixed design ANOVA as in previous sections, but now we are testing for an effect of sex.
sexLearningGenANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.7327354 0.3965332 0.0018597270
## 3 block 2 90 0.4631174 0.6308100 0.0024133324
## 5 target 2 90 0.1638843 0.8490930 0.0007099319
## 4 sex:block 2 90 0.4646060 0.6298813 0.0024210709
## 6 sex:target 2 90 0.6410423 0.5291310 0.0027712090
## 7 block:target 4 180 0.1789585 0.9490442 0.0018079248
## 8 sex:block:target 4 180 0.4662077 0.7604782 0.0046962273
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.995674675 9.090424e-01
## 4 sex:block 0.995674675 9.090424e-01
## 5 target 0.092146331 1.653930e-23 *
## 6 sex:target 0.092146331 1.653930e-23 *
## 7 block:target 0.003236548 2.811784e-48 *
## 8 sex:block:target 0.003236548 2.811784e-48 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9956933 0.6299823 1.0416958 0.6308100
## 4 sex:block 0.9956933 0.6290549 1.0416958 0.6298813
## 5 target 0.5241492 0.6994195 0.5258241 0.7002216
## 6 sex:target 0.5241492 0.4343754 0.5258241 0.4348381
## 7 block:target 0.5099576 0.8405031 0.5344031 0.8499864
## 8 sex:block:target 0.5099576 0.6326529 0.5344031 0.6416070## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.3560356 0.55370648 0.0009720123
## 3 block 2 90 0.7621760 0.46963787 0.0039016884
## 5 target 2 90 4.0360449 0.02095891 * 0.0164441352
## 4 sex:block 2 90 1.1484789 0.32172184 0.0058676251
## 6 sex:target 2 90 0.5184609 0.59720376 0.0021430893
## 7 block:target 4 180 0.9787513 0.42047813 0.0098920992
## 8 sex:block:target 4 180 1.2714806 0.28290190 0.0128127650
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.765527656 2.799880e-03 *
## 4 sex:block 0.765527656 2.799880e-03 *
## 5 target 0.100932219 1.226468e-22 *
## 6 sex:target 0.100932219 1.226468e-22 *
## 7 block:target 0.002085234 2.768933e-52 *
## 8 sex:block:target 0.002085234 2.768933e-52 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8100627 0.44483122 0.8359380 0.44854442
## 4 sex:block 0.8100627 0.31384584 0.8359380 0.31513007
## 5 target 0.5265741 0.04829586 * 0.5284204 0.04814184
## 6 sex:target 0.5265741 0.48415018 0.5284204 0.48475489
## 7 block:target 0.4257628 0.36872163 0.4407953 0.37115412
## 8 sex:block:target 0.4257628 0.28270338 0.4407953 0.28338849
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.03439144 0.8537100 0.0001187453
## 3 block 2 90 1.72698125 0.1836604 0.0072566043
## 5 target 2 90 0.70240387 0.4980881 0.0038914176
## 4 sex:block 2 90 0.77310214 0.4646196 0.0032615714
## 6 sex:target 2 90 0.06968755 0.9327355 0.0003874371
## 7 block:target 4 180 1.18114464 0.3206741 0.0104891744
## 8 sex:block:target 4 180 1.12692679 0.3453068 0.0100125127
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.959969661 4.070663e-01
## 4 sex:block 0.959969661 4.070663e-01
## 5 target 0.058653110 7.987354e-28 *
## 6 sex:target 0.058653110 7.987354e-28 *
## 7 block:target 0.009337512 1.169884e-38 *
## 8 sex:block:target 0.009337512 1.169884e-38 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9615104 0.1850524 1.0035402 0.1836604
## 4 sex:block 0.9615104 0.4601151 1.0035402 0.4646196
## 5 target 0.5151063 0.4103382 0.5161474 0.4106049
## 6 sex:target 0.5151063 0.8004098 0.5161474 0.8009091
## 7 block:target 0.4942466 0.3113168 0.5168244 0.3125299
## 8 sex:block:target 0.4942466 0.3281233 0.5168244 0.3297665## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.1195958 0.7310849 0.000377590
## 3 block 2 90 1.7307175 0.1830008 0.008143596
## 5 target 2 90 1.0962126 0.3385534 0.005743971
## 4 sex:block 2 90 1.8929920 0.1565690 0.008900355
## 6 sex:target 2 90 0.4846917 0.6174853 0.002547868
## 7 block:target 4 180 0.9412008 0.4413875 0.008445689
## 8 sex:block:target 4 180 1.8778402 0.1162237 0.016710004
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.939173273 2.514235e-01
## 4 sex:block 0.939173273 2.514235e-01
## 5 target 0.057886873 5.980836e-28 *
## 6 sex:target 0.057886873 5.980836e-28 *
## 7 block:target 0.002598048 2.800456e-50 *
## 8 sex:block:target 0.002598048 2.800456e-50 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9426610 0.1850780 0.9825519 0.1836403
## 4 sex:block 0.9426610 0.1592259 0.9825519 0.1573800
## 5 target 0.5149031 0.3026071 0.5159300 0.3027362
## 6 sex:target 0.5149031 0.4951778 0.5159300 0.4955373
## 7 block:target 0.4834970 0.3914421 0.5048265 0.3946830
## 8 sex:block:target 0.4834970 0.1603691 0.5048265 0.1584204## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.7947679 0.3774045 0.0030117592
## 3 block 2 90 0.6778672 0.5102715 0.0028072788
## 5 target 2 90 0.7089492 0.4948886 0.0040211170
## 4 sex:block 2 90 0.1270986 0.8808047 0.0005275617
## 6 sex:target 2 90 1.7011574 0.1882865 0.0095948651
## 7 block:target 4 180 0.4407418 0.7790432 0.0037644552
## 8 sex:block:target 4 180 0.2593759 0.9036320 0.0022188131
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.923415300 1.732748e-01
## 4 sex:block 0.923415300 1.732748e-01
## 5 target 0.069360309 3.194791e-26 *
## 6 sex:target 0.069360309 3.194791e-26 *
## 7 block:target 0.001734237 5.757921e-54 *
## 8 sex:block:target 0.001734237 5.757921e-54 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9288633 0.5000307 0.9672117 0.5056424
## 4 sex:block 0.9288633 0.8666006 0.9672117 0.8744831
## 5 target 0.5179630 0.4088609 0.5192035 0.4091737
## 6 sex:target 0.5179630 0.1988807 0.5192035 0.1988859
## 7 block:target 0.4597179 0.6284363 0.4783708 0.6362502
## 8 sex:block:target 0.4597179 0.7536441 0.4783708 0.7624327sexLearningGenBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.06191109 ±1.72%
## [2] block + participant : 0.03762568 ±0.65%
## [3] target + block + participant : 0.002271487 ±1.61%
## [4] target + block + target:block + participant : 2.827132e-05 ±1.84%
## [5] sex + participant : 0.2054171 ±0.87%
## [6] target + sex + participant : 0.01249931 ±1.73%
## [7] block + sex + participant : 0.009573891 ±19.52%
## [8] target + block + sex + participant : 0.000475559 ±1.78%
## [9] target + block + target:block + sex + participant : 5.645404e-06 ±1.66%
## [10] target + sex + target:sex + participant : 0.001422147 ±2.16%
## [11] target + block + sex + target:sex + participant : 5.24356e-05 ±4.58%
## [12] target + block + target:block + sex + target:sex + participant : 6.274736e-07 ±2.61%
## [13] block + sex + block:sex + participant : 0.0007457495 ±2.07%
## [14] target + block + sex + block:sex + participant : 4.726728e-05 ±3.88%
## [15] target + block + target:block + sex + block:sex + participant : 5.338305e-07 ±1.62%
## [16] target + block + sex + target:sex + block:sex + participant : 4.988874e-06 ±2.55%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 6.118677e-08 ±3.03%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 5.730473e-09 ±15.1%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.06 0.022
## block 0.74 0.04 0.014
## block:target 0.32 2.64e-05 5.72e-05
## sex 0.74 0.17 0.075
## sex:target 0.32 1.11e-03 0.002
## block:sex 0.32 6.00e-04 0.001
## block:sex:target 0.05 4.30e-09 7.74e-08
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 18.67132 ±0.97%
## [2] block + participant : 0.07482997 ±0.69%
## [3] target + block + participant : 1.448521 ±2.26%
## [4] target + block + target:block + participant : 0.08597736 ±1.33%
## [5] sex + participant : 0.1859042 ±0.92%
## [6] target + sex + participant : 3.431797 ±1.32%
## [7] block + sex + participant : 0.0141776 ±1.59%
## [8] target + block + sex + participant : 0.2724681 ±1.78%
## [9] target + block + target:block + sex + participant : 0.01981879 ±19.99%
## [10] target + sex + target:sex + participant : 0.3737155 ±2.69%
## [11] target + block + sex + target:sex + participant : 0.03107868 ±5.04%
## [12] target + block + target:block + sex + target:sex + participant : 0.001740984 ±2.58%
## [13] block + sex + block:sex + participant : 0.002686153 ±4.04%
## [14] target + block + sex + block:sex + participant : 0.05035312 ±1.98%
## [15] target + block + target:block + sex + block:sex + participant : 0.003141964 ±3.2%
## [16] target + block + sex + target:sex + block:sex + participant : 0.00541041 ±3.12%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.0003179184 ±3.18%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 8.171789e-05 ±4.21%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.95 6.82
## block 0.74 0.08 0.030
## block:target 0.32 4.33e-03 0.009
## sex 0.74 0.17 0.074
## sex:target 0.32 0.02 0.035
## block:sex 0.32 2.41e-03 0.005
## block:sex:target 0.05 3.18e-06 5.73e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.1215326 ±0.77%
## [2] block + participant : 0.06351845 ±1.51%
## [3] target + block + participant : 0.007688088 ±1.24%
## [4] target + block + target:block + participant : 0.0001610552 ±1.21%
## [5] sex + participant : 0.1785838 ±0.98%
## [6] target + sex + participant : 0.02158443 ±1.35%
## [7] block + sex + participant : 0.01130841 ±1.51%
## [8] target + block + sex + participant : 0.001380921 ±2.37%
## [9] target + block + target:block + sex + participant : 2.979037e-05 ±2.19%
## [10] target + sex + target:sex + participant : 0.001555802 ±1.9%
## [11] target + block + sex + target:sex + participant : 0.0001040941 ±3.04%
## [12] target + block + target:block + sex + target:sex + participant : 1.988855e-06 ±1.89%
## [13] block + sex + block:sex + participant : 0.001609623 ±17.08%
## [14] target + block + sex + block:sex + participant : 0.0001513511 ±1.69%
## [15] target + block + target:block + sex + block:sex + participant : 3.333032e-06 ±2.95%
## [16] target + block + sex + target:sex + block:sex + participant : 1.081289e-05 ±2.92%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2.307968e-07 ±3.6%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 3.093224e-08 ±2.53%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.11 0.044
## block 0.74 0.06 0.023
## block:target 0.32 1.39e-04 3.02e-04
## sex 0.74 0.15 0.065
## sex:target 0.32 1.19e-03 0.003
## block:sex 0.32 1.26e-03 0.003
## block:sex:target 0.05 2.19e-08 3.95e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.3787354 ±0.64%
## [2] block + participant : 0.09036497 ±0.64%
## [3] target + block + participant : 0.03527956 ±1.25%
## [4] target + block + target:block + participant : 0.001247271 ±2.01%
## [5] sex + participant : 0.1796093 ±0.95%
## [6] target + sex + participant : 0.07453354 ±5.28%
## [7] block + sex + participant : 0.01665878 ±1.72%
## [8] target + block + sex + participant : 0.007260645 ±8.79%
## [9] target + block + target:block + sex + participant : 0.0002285441 ±1.94%
## [10] target + sex + target:sex + participant : 0.007531205 ±3.47%
## [11] target + block + sex + target:sex + participant : 0.0007124003 ±3.38%
## [12] target + block + target:block + sex + target:sex + participant : 2.457302e-05 ±2.18%
## [13] block + sex + block:sex + participant : 0.005277249 ±1.95%
## [14] target + block + sex + block:sex + participant : 0.002097573 ±2.73%
## [15] target + block + target:block + sex + block:sex + participant : 8.138993e-05 ±8.63%
## [16] target + block + sex + target:sex + block:sex + participant : 0.0002293596 ±7.01%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 7.81396e-06 ±2.6%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 3.39828e-06 ±2.1%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.28 0.140
## block 0.74 0.09 0.035
## block:target 0.32 8.85e-04 0.002
## sex 0.74 0.16 0.070
## sex:target 0.32 4.73e-03 0.010
## block:sex 0.32 4.28e-03 0.009
## block:sex:target 0.05 1.89e-06 3.40e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.02987538 ±1.49%
## [2] block + participant : 0.09177784 ±1.85%
## [3] target + block + participant : 0.002595956 ±0.95%
## [4] target + block + target:block + participant : 0.0001066024 ±1.98%
## [5] sex + participant : 0.2437689 ±2.47%
## [6] target + sex + participant : 0.01218148 ±41.81%
## [7] block + sex + participant : 0.0219303 ±1.3%
## [8] target + block + sex + participant : 0.0006507466 ±2.04%
## [9] target + block + target:block + sex + participant : 2.631244e-05 ±3.87%
## [10] target + sex + target:sex + participant : 0.0028514 ±3.35%
## [11] target + block + sex + target:sex + participant : 0.0002503107 ±2.74%
## [12] target + block + target:block + sex + target:sex + participant : 1.0221e-05 ±2.69%
## [13] block + sex + block:sex + participant : 0.001580336 ±1.74%
## [14] target + block + sex + block:sex + participant : 4.599237e-05 ±2.54%
## [15] target + block + target:block + sex + block:sex + participant : 1.846496e-06 ±3.56%
## [16] target + block + sex + target:sex + block:sex + participant : 1.83849e-05 ±3.04%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 7.216696e-07 ±2.03%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 5.239262e-08 ±10.37%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.013
## block 0.74 0.08 0.033
## block:target 0.32 1.04e-04 2.24e-04
## sex 0.74 0.20 0.090
## sex:target 0.32 2.22e-03 0.005
## block:sex 0.32 1.17e-03 0.003
## block:sex:target 0.05 3.72e-08 6.70e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any sex effects. We then test washout trials.
sexWashoutLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.1253640 7.249418e-01 0.0005039222
## 3 block 2 90 15.2002255 2.054224e-06 * 0.0437342442
## 5 target 2 90 5.4868713 5.643292e-03 * 0.0265680918
## 4 sex:block 2 90 2.5425953 8.430110e-02 0.0075920745
## 6 sex:target 2 90 2.9671860 5.650310e-02 0.0145449290
## 7 block:target 4 180 1.6545768 1.625712e-01 0.0166245041
## 8 sex:block:target 4 180 0.9797533 4.199305e-01 0.0099113587
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8619896 0.03811050 *
## 4 sex:block 0.8619896 0.03811050 *
## 5 target 0.8284961 0.01593639 *
## 6 sex:target 0.8284961 0.01593639 *
## 7 block:target 0.7181735 0.10991735
## 8 sex:block:target 0.7181735 0.10991735
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8787266 6.934488e-06 * 0.9116351 4.982749e-06
## 4 sex:block 0.8787266 9.185405e-02 0.9116351 8.975061e-02
## 5 target 0.8536036 8.571178e-03 * 0.8838831 7.859984e-03
## 6 sex:target 0.8536036 6.539613e-02 0.8838831 6.345410e-02
## 7 block:target 0.8579514 1.722555e-01 0.9373937 1.667886e-01
## 8 sex:block:target 0.8579514 4.118549e-01 0.9373937 4.165791e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8sexWashoutLearningBayesANOVA()## Quadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 1.21681 ±0.94%
## [2] block + participant : 364.3362 ±0.74%
## [3] target + block + participant : 582.7229 ±8.75%
## [4] target + block + target:block + participant : 33.29635 ±1.25%
## [5] sex + participant : 0.1911313 ±1.72%
## [6] target + sex + participant : 0.2309843 ±1.86%
## [7] block + sex + participant : 71.05202 ±1.77%
## [8] target + block + sex + participant : 109.9522 ±6.59%
## [9] target + block + target:block + sex + participant : 6.572297 ±2.42%
## [10] target + sex + target:sex + participant : 0.187671 ±2.63%
## [11] target + block + sex + target:sex + participant : 94.58403 ±2.61%
## [12] target + block + target:block + sex + target:sex + participant : 6.105671 ±2.61%
## [13] block + sex + block:sex + participant : 16.47129 ±1.63%
## [14] target + block + sex + block:sex + participant : 24.13539 ±1.54%
## [15] target + block + target:block + sex + block:sex + participant : 1.706983 ±5.12%
## [16] target + block + sex + target:sex + block:sex + participant : 21.61206 ±1.65%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1.565522 ±4.82%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.2113259 ±7.1%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.66 0.697
## block 0.74 1.00 168.59
## block:target 0.32 0.04 0.083
## sex 0.74 0.27 0.129
## sex:target 0.32 0.09 0.222
## block:sex 0.32 0.05 0.112
## block:sex:target 0.05 1.58e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equalWe also do not find any effect of sex.
Completion time
plotSexCtrlGenMT()
Next we repeat the same tests but now have completion time as the dependent variable.
sexGenmovementtimeANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 3.1625582 8.210173e-02 0.033052047
## 3 block 2 90 17.6669705 3.371488e-07 * 0.051245239
## 5 target 2 90 13.7237043 6.279979e-06 * 0.051407984
## 4 sex:block 2 90 1.1284253 3.280763e-01 0.003438069
## 6 sex:target 2 90 0.5599547 5.732121e-01 0.002206345
## 7 block:target 4 180 5.9836035 1.525590e-04 * 0.025696274
## 8 sex:block:target 4 180 0.4518930 7.709246e-01 0.001987854
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8781263 0.0573130231
## 4 sex:block 0.8781263 0.0573130231
## 5 target 0.9662090 0.4694219302
## 6 sex:target 0.9662090 0.4694219302
## 7 block:target 0.4751952 0.0001785472 *
## 8 sex:block:target 0.4751952 0.0001785472 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8913659 1.206476e-06 * 0.9256215 8.068004e-07
## 4 sex:block 0.8913659 3.235836e-01 0.9256215 3.251112e-01
## 5 target 0.9673135 8.420703e-06 * 1.0100091 6.279979e-06
## 6 sex:target 0.9673135 5.676002e-01 1.0100091 5.732121e-01
## 7 block:target 0.7428166 7.699589e-04 * 0.8011082 5.324730e-04
## 8 sex:block:target 0.7428166 7.145272e-01 0.8011082 7.290136e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 1.3824551 2.458666e-01 0.014638662
## 3 block 2 90 11.9088667 2.579087e-05 * 0.029229957
## 5 target 2 90 26.9053129 6.923393e-10 * 0.115384637
## 4 sex:block 2 90 0.5671685 5.691427e-01 0.001431961
## 6 sex:target 2 90 0.6175276 5.415452e-01 0.002984789
## 7 block:target 4 180 1.3506508 2.529995e-01 0.005506810
## 8 sex:block:target 4 180 0.2470017 9.111936e-01 0.001011616
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9565352 0.3762021468
## 4 sex:block 0.9565352 0.3762021468
## 5 target 0.8687653 0.0452745848 *
## 6 sex:target 0.8687653 0.0452745848 *
## 7 block:target 0.4762550 0.0001855554 *
## 8 sex:block:target 0.4762550 0.0001855554 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9583457 3.548876e-05 * 1.0000138 2.579087e-05
## 4 sex:block 0.9583457 5.620362e-01 1.0000138 5.691427e-01
## 5 target 0.8839899 5.372273e-09 * 0.9174573 2.973441e-09
## 6 sex:target 0.8839899 5.225551e-01 0.9174573 5.282669e-01
## 7 block:target 0.7104402 2.616754e-01 0.7633205 2.603570e-01
## 8 sex:block:target 0.7104402 8.532926e-01 0.7633205 8.665554e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 3.2042254 0.080178153 0.0171858674
## 3 block 2 90 2.6881593 0.073466259 0.0101508028
## 5 target 2 90 4.9318178 0.009280709 * 0.0247133101
## 4 sex:block 2 90 0.9951759 0.373689017 0.0037820786
## 6 sex:target 2 90 0.1656925 0.847564588 0.0008505992
## 7 block:target 4 180 0.5258492 0.716862342 0.0040911912
## 8 sex:block:target 4 180 0.6571479 0.622573399 0.0051074993
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.396124899 1.420061e-09 *
## 4 sex:block 0.396124899 1.420061e-09 *
## 5 target 0.474439378 7.515814e-08 *
## 6 sex:target 0.474439378 7.515814e-08 *
## 7 block:target 0.003929628 1.639828e-46 *
## 8 sex:block:target 0.003929628 1.639828e-46 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6234899 0.09889946 0.6326543 0.09822122
## 4 sex:block 0.6234899 0.34099379 0.6326543 0.34208838
## 5 target 0.6554967 0.02152382 * 0.6672811 0.02091204
## 6 sex:target 0.6554967 0.75292853 0.6672811 0.75721062
## 7 block:target 0.2945556 0.50022125 0.2977870 0.50210299
## 8 sex:block:target 0.2945556 0.44508021 0.2977870 0.44663056
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.2107667 6.483771e-01 0.002119968
## 3 block 2 90 1.0265326 3.624028e-01 0.003712981
## 5 target 2 90 21.0153926 3.239878e-08 * 0.084215222
## 4 sex:block 2 90 0.9241990 4.005821e-01 0.003344077
## 6 sex:target 2 90 1.5467562 2.185441e-01 0.006722828
## 7 block:target 4 180 0.2844534 8.877923e-01 0.001175167
## 8 sex:block:target 4 180 0.5080282 7.298892e-01 0.002096889
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8252798 0.01462941 *
## 4 sex:block 0.8252798 0.01462941 *
## 5 target 0.9934583 0.86555016
## 6 sex:target 0.9934583 0.86555016
## 7 block:target 0.7470884 0.17895955
## 8 sex:block:target 0.7470884 0.17895955
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8512665 3.529128e-01 0.8813047 3.550193e-01
## 4 sex:block 0.8512665 3.876755e-01 0.8813047 3.904966e-01
## 5 target 0.9935008 3.547370e-08 * 1.0392449 3.239878e-08
## 6 sex:target 0.9935008 2.186817e-01 1.0392449 2.185441e-01
## 7 block:target 0.8682391 8.636458e-01 0.9497184 8.792202e-01
## 8 sex:block:target 0.8682391 7.041622e-01 0.9497184 7.205130e-01
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.4130008 5.237114e-01 0.002845752
## 3 block 2 90 7.0375631 1.446440e-03 * 0.028863947
## 5 target 2 90 10.2558715 9.717032e-05 * 0.040919348
## 4 sex:block 2 90 1.0827314 3.430390e-01 0.004551900
## 6 sex:target 2 90 0.2978642 7.431312e-01 0.001237603
## 7 block:target 4 180 1.8817598 1.155333e-01 0.012870426
## 8 sex:block:target 4 180 0.2571671 9.049948e-01 0.001778676
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8340194 1.844486e-02 *
## 4 sex:block 0.8340194 1.844486e-02 *
## 5 target 0.7280056 9.267522e-04 *
## 6 sex:target 0.7280056 9.267522e-04 *
## 7 block:target 0.1644314 3.620330e-13 *
## 8 sex:block:target 0.1644314 3.620330e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8576472 0.0025676273 * 0.8883455 0.0022681503
## 4 sex:block 0.8576472 0.3356590916 0.8883455 0.3374190370
## 5 target 0.7861670 0.0003870587 * 0.8097069 0.0003322597
## 6 sex:target 0.7861670 0.6900447188 0.8097069 0.6966358913
## 7 block:target 0.5042889 0.1578713860 0.5280546 0.1556793670
## 8 sex:block:target 0.5042889 0.7756610946 0.5280546 0.7855918382
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.8973162 3.485617e-01 0.0080123253
## 3 block 2 90 52.8052594 6.733854e-16 * 0.1068858738
## 5 target 2 90 4.5196989 1.347576e-02 * 0.0170611070
## 4 sex:block 2 90 0.3869188 6.802704e-01 0.0008761436
## 6 sex:target 2 90 1.4352012 2.434631e-01 0.0054814676
## 7 block:target 4 180 2.9913949 2.016581e-02 * 0.0208377462
## 8 sex:block:target 4 180 1.2202005 3.038514e-01 0.0086059699
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8819925 6.312876e-02
## 4 sex:block 0.8819925 6.312876e-02
## 5 target 0.7292377 9.618787e-04 *
## 6 sex:target 0.7292377 9.618787e-04 *
## 7 block:target 0.1150371 2.952720e-16 *
## 8 sex:block:target 0.1150371 2.952720e-16 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8944484 1.804840e-14 * 0.9290349 6.141505e-15
## 4 sex:block 0.8944484 6.571794e-01 0.9290349 6.650429e-01
## 5 target 0.7869292 2.121207e-02 * 0.8105428 2.016990e-02
## 6 sex:target 0.7869292 2.441048e-01 0.8105428 2.441910e-01
## 7 block:target 0.5108774 5.402493e-02 0.5354339 5.138971e-02
## 8 sex:block:target 0.5108774 3.004504e-01 0.5354339 3.013470e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8sexGenmovementtimeBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 519413086 ±0.77%
## [2] block + participant : 410032481 ±0.57%
## [3] target + block + participant : 7.238111e+18 ±3.92%
## [4] target + block + target:block + participant : 3.014143e+20 ±1.68%
## [5] sex + participant : 0.9729114 ±1.69%
## [6] target + sex + participant : 519250940 ±1.61%
## [7] block + sex + participant : 411771038 ±1.16%
## [8] target + block + sex + participant : 7.353663e+18 ±2.02%
## [9] target + block + target:block + sex + participant : 3.271212e+20 ±3.05%
## [10] target + sex + target:sex + participant : 66283710 ±1.44%
## [11] target + block + sex + target:sex + participant : 1.022201e+18 ±2.16%
## [12] target + block + target:block + sex + target:sex + participant : 4.833487e+19 ±6.25%
## [13] block + sex + block:sex + participant : 73083027 ±2.31%
## [14] target + block + sex + block:sex + participant : 1.61054e+18 ±5.25%
## [15] target + block + target:block + sex + block:sex + participant : 7.022828e+19 ±4.79%
## [16] target + block + sex + target:sex + block:sex + participant : 2.046195e+17 ±1.85%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 9.822067e+18 ±2.65%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 5.925357e+17 ±3.21%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 3.09e+11
## block 0.74 1.00 2.50e+11
## block:target 0.32 0.98 94.17
## sex 0.74 0.60 0.540
## sex:target 0.32 0.08 0.182
## block:sex 0.32 0.11 0.258
## block:sex:target 0.05 7.65e-04 0.014
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 2.254819e+17 ±0.59%
## [2] block + participant : 388.7443 ±0.7%
## [3] target + block + participant : 1.336029e+21 ±1.58%
## [4] target + block + target:block + participant : 1.246402e+20 ±1.66%
## [5] sex + participant : 0.4823906 ±1.13%
## [6] target + sex + participant : 1.172015e+17 ±1.19%
## [7] block + sex + participant : 193.9111 ±2.14%
## [8] target + block + sex + participant : 7.74902e+20 ±11.27%
## [9] target + block + target:block + sex + participant : 7.177222e+19 ±7.86%
## [10] target + sex + target:sex + participant : 1.533754e+16 ±1.62%
## [11] target + block + sex + target:sex + participant : 9.4004e+19 ±3.21%
## [12] target + block + target:block + sex + target:sex + participant : 1.011076e+19 ±6.72%
## [13] block + sex + block:sex + participant : 16.76296 ±1.99%
## [14] target + block + sex + block:sex + participant : 6.533467e+19 ±1.75%
## [15] target + block + target:block + sex + block:sex + participant : 6.254482e+18 ±2.09%
## [16] target + block + sex + target:sex + block:sex + participant : 8.950886e+18 ±2.35%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 8.984474e+17 ±2.78%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 4.926504e+16 ±3.11%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 1.48e+18
## block 0.74 1.00 2.49e+03
## block:target 0.32 0.09 0.203
## sex 0.74 0.41 0.252
## sex:target 0.32 0.05 0.104
## block:sex 0.32 0.03 0.073
## block:sex:target 0.05 1.98e-05 3.56e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 198.7605 ±1.06%
## [2] block + participant : 5.405143 ±0.68%
## [3] target + block + participant : 1450.737 ±1.75%
## [4] target + block + target:block + participant : 228.7985 ±4.43%
## [5] sex + participant : 0.6937137 ±0.82%
## [6] target + sex + participant : 141.5704 ±1.2%
## [7] block + sex + participant : 3.985267 ±3.04%
## [8] target + block + sex + participant : 1009.219 ±1.9%
## [9] target + block + target:block + sex + participant : 159.4558 ±1.78%
## [10] target + sex + target:sex + participant : 23.17009 ±50.32%
## [11] target + block + sex + target:sex + participant : 81.90127 ±1.84%
## [12] target + block + target:block + sex + target:sex + participant : 13.01075 ±1.87%
## [13] block + sex + block:sex + participant : 0.6229009 ±6.81%
## [14] target + block + sex + block:sex + participant : 164.9381 ±2.33%
## [15] target + block + target:block + sex + block:sex + participant : 25.03181 ±2.26%
## [16] target + block + sex + target:sex + block:sex + participant : 13.15643 ±2.2%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2.01101 ±1.75%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.2619029 ±2.31%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 107.14
## block 0.74 0.90 3.09
## block:target 0.32 0.12 0.300
## sex 0.74 0.47 0.311
## sex:target 0.32 0.04 0.085
## block:sex 0.32 0.06 0.135
## block:sex:target 0.05 7.43e-05 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 22539580597 ±0.65%
## [2] block + participant : 0.5519082 ±0.75%
## [3] target + block + participant : 20142452103 ±1.1%
## [4] target + block + target:block + participant : 506700526 ±1.34%
## [5] sex + participant : 0.3005272 ±1.13%
## [6] target + sex + participant : 7142606005 ±1.18%
## [7] block + sex + participant : 0.1676832 ±1.44%
## [8] target + block + sex + participant : 6540033898 ±1.34%
## [9] target + block + target:block + sex + participant : 155457769 ±1.81%
## [10] target + sex + target:sex + participant : 2419881689 ±1.81%
## [11] target + block + sex + target:sex + participant : 2328080835 ±2.09%
## [12] target + block + target:block + sex + target:sex + participant : 54877300 ±2.01%
## [13] block + sex + block:sex + participant : 0.02577969 ±1.66%
## [14] target + block + sex + block:sex + participant : 1201284494 ±2.19%
## [15] target + block + target:block + sex + block:sex + participant : 29631718 ±2.26%
## [16] target + block + sex + target:sex + block:sex + participant : 432809956 ±2.46%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 10343227 ±3.19%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 769550.8 ±3.48%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 1.11e+10
## block 0.74 0.49 0.349
## block:target 0.32 0.01 0.026
## sex 0.74 0.32 0.168
## sex:target 0.32 0.08 0.195
## block:sex 0.32 0.03 0.059
## block:sex:target 0.05 1.21e-05 2.18e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 11889.78 ±0.74%
## [2] block + participant : 48.99769 ±0.65%
## [3] target + block + participant : 1003126 ±1.3%
## [4] target + block + target:block + participant : 408054.3 ±1.36%
## [5] sex + participant : 0.2649064 ±0.93%
## [6] target + sex + participant : 3203.861 ±1.94%
## [7] block + sex + participant : 12.9434 ±1.47%
## [8] target + block + sex + participant : 285347.8 ±3%
## [9] target + block + target:block + sex + participant : 112257.3 ±1.39%
## [10] target + sex + target:sex + participant : 263.1008 ±1.89%
## [11] target + block + sex + target:sex + participant : 23296.47 ±5.12%
## [12] target + block + target:block + sex + target:sex + participant : 13052.2 ±25.83%
## [13] block + sex + block:sex + participant : 2.069222 ±1.82%
## [14] target + block + sex + block:sex + participant : 44758.36 ±2.43%
## [15] target + block + target:block + sex + block:sex + participant : 18742.47 ±2.36%
## [16] target + block + sex + target:sex + block:sex + participant : 3626.719 ±1.91%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1541.114 ±2.61%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 102.7875 ±6.96%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 1.06e+04
## block 0.74 0.99 44.51
## block:target 0.32 0.29 0.872
## sex 0.74 0.26 0.127
## sex:target 0.32 0.02 0.048
## block:sex 0.32 0.04 0.080
## block:sex:target 0.05 5.33e-05 9.59e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 4.024578 ±1.12%
## [2] block + participant : 1.162382e+17 ±0.97%
## [3] target + block + participant : 1.781924e+18 ±1.31%
## [4] target + block + target:block + participant : 2.925877e+20 ±1.1%
## [5] sex + participant : 0.3492872 ±1.14%
## [6] target + sex + participant : 1.405716 ±1.24%
## [7] block + sex + participant : 4.463465e+16 ±2.02%
## [8] target + block + sex + participant : 6.788675e+17 ±2.45%
## [9] target + block + target:block + sex + participant : 1.139469e+20 ±1.99%
## [10] target + sex + target:sex + participant : 0.2689513 ±2.53%
## [11] target + block + sex + target:sex + participant : 1.791187e+17 ±3.71%
## [12] target + block + target:block + sex + target:sex + participant : 3.05118e+19 ±1.78%
## [13] block + sex + block:sex + participant : 4.086204e+15 ±5.06%
## [14] target + block + sex + block:sex + participant : 6.882095e+16 ±16.16%
## [15] target + block + target:block + sex + block:sex + participant : 1.003002e+19 ±1.94%
## [16] target + block + sex + target:sex + block:sex + participant : 1.500218e+16 ±2.3%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2.684611e+18 ±2.2%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.071579e+18 ±9.83%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 981.97
## block 0.74 1.00 2.30e+19
## block:target 0.32 0.99 338.15
## sex 0.74 0.35 0.193
## sex:target 0.32 0.08 0.178
## block:sex 0.32 0.03 0.068
## block:sex:target 0.05 2.36e-03 0.043
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no sex effects for completion time.
Path length
plotSexCtrlGenPL()
Then we conduct tests with path length as the dependent variable.
sexGenpathlengthANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.03913817 8.440662e-01 0.0002505818
## 3 block 2 90 21.40299449 2.489535e-08 * 0.0683760248
## 5 target 2 90 11.10292834 4.900205e-05 * 0.0438808645
## 4 sex:block 2 90 0.31396031 7.313449e-01 0.0010754645
## 6 sex:target 2 90 0.58651009 5.583771e-01 0.0024185189
## 7 block:target 4 180 3.73305461 6.057686e-03 * 0.0298964636
## 8 sex:block:target 4 180 0.51100591 7.277112e-01 0.0042008297
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9894036 7.910741e-01
## 4 sex:block 0.9894036 7.910741e-01
## 5 target 0.9183769 1.536246e-01
## 6 sex:target 0.9183769 1.536246e-01
## 7 block:target 0.3703685 2.088371e-06 *
## 8 sex:block:target 0.3703685 2.088371e-06 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9895148 2.889325e-08 * 1.0347902 2.489535e-08
## 4 sex:block 0.9895148 7.290689e-01 1.0347902 7.313449e-01
## 5 target 0.9245365 8.357896e-05 * 0.9624052 6.392440e-05
## 6 sex:target 0.9245365 5.456642e-01 0.9624052 5.521623e-01
## 7 block:target 0.7055986 1.473098e-02 * 0.7576896 1.257088e-02
## 8 sex:block:target 0.7055986 6.642340e-01 0.7576896 6.772237e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.4893904 4.878000e-01 0.0034564142
## 3 block 2 90 3.4624001 3.559113e-02 * 0.0122484469
## 5 target 2 90 19.3679906 1.010218e-07 * 0.0869632841
## 4 sex:block 2 90 0.1731816 8.412644e-01 0.0006198529
## 6 sex:target 2 90 0.6329142 5.333888e-01 0.0031028324
## 7 block:target 4 180 1.3438030 2.554725e-01 0.0088385182
## 8 sex:block:target 4 180 0.7371760 5.677479e-01 0.0048680084
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9416379 2.663464e-01
## 4 sex:block 0.9416379 2.663464e-01
## 5 target 0.9004667 9.960662e-02
## 6 sex:target 0.9004667 9.960662e-02
## 7 block:target 0.4141565 1.583312e-05 *
## 8 sex:block:target 0.4141565 1.583312e-05 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9448562 3.834300e-02 * 0.9849943 3.631967e-02
## 4 sex:block 0.9448562 8.294261e-01 0.9849943 8.381426e-01
## 5 target 0.9094768 3.241234e-07 * 0.9456911 2.032557e-07
## 6 sex:target 0.9094768 5.191385e-01 0.9456911 5.249958e-01
## 7 block:target 0.6940062 2.641312e-01 0.7442285 2.630089e-01
## 8 sex:block:target 0.6940062 5.219560e-01 0.7442285 5.306512e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.06107874 0.805923085 0.0005111974
## 3 block 2 90 0.34340100 0.710279053 0.0012021316
## 5 target 2 90 6.15745139 0.003116468 * 0.0276278785
## 4 sex:block 2 90 1.68829150 0.190635572 0.0058824471
## 6 sex:target 2 90 0.36028515 0.698478751 0.0016597359
## 7 block:target 4 180 0.38891799 0.816398225 0.0022232335
## 8 sex:block:target 4 180 0.94661679 0.438325244 0.0053940988
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9690089 0.50027749
## 4 sex:block 0.9690089 0.50027749
## 5 target 0.9416220 0.26624700
## 6 sex:target 0.9416220 0.26624700
## 7 block:target 0.6151913 0.01230653 *
## 8 sex:block:target 0.6151913 0.01230653 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9699405 0.703774559 1.0129387 0.710279053
## 4 sex:block 0.9699405 0.191637891 1.0129387 0.190635572
## 5 target 0.9448420 0.003750484 * 0.9849784 0.003277545
## 6 sex:target 0.9448420 0.686504095 0.9849784 0.695289172
## 7 block:target 0.8134723 0.777118358 0.8843871 0.793262447
## 8 sex:block:target 0.8134723 0.425379880 0.8843871 0.430701645
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.3066247 0.5824999997 0.003012967
## 3 block 2 90 9.0069199 0.0002718565 * 0.031904172
## 5 target 2 90 8.7118540 0.0003478617 * 0.037498894
## 4 sex:block 2 90 3.0400969 0.0527702001 0.011001099
## 6 sex:target 2 90 0.8974529 0.4112224442 0.003997411
## 7 block:target 4 180 1.8212825 0.1266267942 0.007654671
## 8 sex:block:target 4 180 0.6496438 0.6278379076 0.002743901
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8431721 0.02345078 *
## 4 sex:block 0.8431721 0.02345078 *
## 5 target 0.8444511 0.02424596 *
## 6 sex:target 0.8444511 0.02424596 *
## 7 block:target 0.7445814 0.17193504
## 8 sex:block:target 0.7445814 0.17193504
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8644328 0.0005745969 * 0.8958376 0.0004829812
## 4 sex:block 0.8644328 0.0608413851 0.8958376 0.0588719270
## 5 target 0.8653896 0.0007098163 * 0.8968944 0.0006005076
## 6 sex:target 0.8653896 0.3988036760 0.8968944 0.4019070230
## 7 block:target 0.8594638 0.1373448259 0.9392040 0.1311604299
## 8 sex:block:target 0.8594638 0.6049205111 0.9392040 0.6183171935
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.01450175 9.046840e-01 0.0001113618
## 3 block 2 90 10.90426278 5.748328e-05 * 0.0292637417
## 5 target 2 90 6.32319061 2.694319e-03 * 0.0290190045
## 4 sex:block 2 90 2.30713107 1.054061e-01 0.0063378696
## 6 sex:target 2 90 0.29339380 7.464389e-01 0.0013847922
## 7 block:target 4 180 2.11958827 8.019614e-02 0.0147253769
## 8 sex:block:target 4 180 0.07914692 9.886186e-01 0.0005577626
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8327128 0.017819501 *
## 4 sex:block 0.8327128 0.017819501 *
## 5 target 0.8648896 0.041033181 *
## 6 sex:target 0.8648896 0.041033181 *
## 7 block:target 0.5617444 0.002949464 *
## 8 sex:block:target 0.5617444 0.002949464 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8566872 0.0001553323 * 0.8872859 0.0001255783
## 4 sex:block 0.8566872 0.1140487902 0.8872859 0.1121681472
## 5 target 0.8809716 0.0040804954 * 0.9141182 0.0036343959
## 6 sex:target 0.8809716 0.7186362254 0.9141182 0.7267956180
## 7 block:target 0.7707451 0.0987743368 0.8338921 0.0932536174
## 8 sex:block:target 0.7707451 0.9733826746 0.8338921 0.9789931352
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.02091602 8.856538e-01 1.024454e-04
## 3 block 2 90 27.44426792 4.947455e-10 * 1.142891e-01
## 5 target 2 90 6.40864851 2.499970e-03 * 2.854136e-02
## 4 sex:block 2 90 0.02101116 9.792128e-01 9.877984e-05
## 6 sex:target 2 90 0.49089507 6.137075e-01 2.245413e-03
## 7 block:target 4 180 4.45947998 1.846774e-03 * 3.460322e-02
## 8 sex:block:target 4 180 1.17457812 3.235777e-01 9.352495e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.22927892 8.472484e-15 *
## 4 sex:block 0.22927892 8.472484e-15 *
## 5 target 0.71255222 5.780526e-04 *
## 6 sex:target 0.71255222 5.780526e-04 *
## 7 block:target 0.03982253 1.283667e-25 *
## 8 sex:block:target 0.03982253 1.283667e-25 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.5647417 1.276467e-06 * 0.5693600 1.173848e-06
## 4 sex:block 0.5647417 9.089931e-01 0.5693600 9.104643e-01
## 5 target 0.7767305 5.533849e-03 * 0.7993641 5.104058e-03
## 6 sex:target 0.7767305 5.670258e-01 0.7993641 5.723080e-01
## 7 block:target 0.4682228 1.624627e-02 * 0.4878196 1.497372e-02
## 8 sex:block:target 0.4682228 3.116649e-01 0.4878196 3.129187e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8sexGenpathlengthBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 256233.8 ±1.08%
## [2] block + participant : 1832794 ±0.84%
## [3] target + block + participant : 2.561073e+12 ±1.61%
## [4] target + block + target:block + participant : 6.757378e+14 ±1.05%
## [5] sex + participant : 0.2100677 ±1.22%
## [6] target + sex + participant : 55061.62 ±3.29%
## [7] block + sex + participant : 385032.1 ±1.06%
## [8] target + block + sex + participant : 561842834051 ±1.59%
## [9] target + block + target:block + sex + participant : 1.592093e+14 ±1.92%
## [10] target + sex + target:sex + participant : 6106.443 ±1.29%
## [11] target + block + sex + target:sex + participant : 72154053176 ±4.16%
## [12] target + block + target:block + sex + target:sex + participant : 1.981476e+13 ±2.65%
## [13] block + sex + block:sex + participant : 27864.75 ±1.41%
## [14] target + block + sex + block:sex + participant : 42216766842 ±2.32%
## [15] target + block + target:block + sex + block:sex + participant : 1.218669e+13 ±4.62%
## [16] target + block + sex + target:sex + block:sex + participant : 5223541241 ±2.54%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1.484931e+12 ±2.92%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 161193713129 ±3.94%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 1.39e+08
## block 0.74 1.00 9.81e+08
## block:target 0.32 1.00 580.40
## sex 0.74 0.22 0.102
## sex:target 0.32 0.02 0.055
## block:sex 0.32 0.02 0.035
## block:sex:target 0.05 1.85e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 6.472445e+13 ±0.92%
## [2] block + participant : 1.978778 ±0.75%
## [3] target + block + participant : 3.118814e+14 ±1.09%
## [4] target + block + target:block + participant : 9.299832e+13 ±1.65%
## [5] sex + participant : 0.3056232 ±11.81%
## [6] target + sex + participant : 1.916257e+13 ±4.11%
## [7] block + sex + participant : 0.5239084 ±1.12%
## [8] target + block + sex + participant : 9.704508e+13 ±7.84%
## [9] target + block + target:block + sex + participant : 3.134732e+13 ±11.06%
## [10] target + sex + target:sex + participant : 2.706268e+12 ±1.61%
## [11] target + block + sex + target:sex + participant : 1.473147e+13 ±6.64%
## [12] target + block + target:block + sex + target:sex + participant : 4.402602e+12 ±4.19%
## [13] block + sex + block:sex + participant : 0.03978654 ±2.63%
## [14] target + block + sex + block:sex + participant : 7.240758e+12 ±2.94%
## [15] target + block + target:block + sex + block:sex + participant : 2.132713e+12 ±3.16%
## [16] target + block + sex + target:sex + block:sex + participant : 1.07613e+12 ±2.42%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 3.17327e+11 ±2.37%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 43177753992 ±8.95%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 6.03e+13
## block 0.74 0.87 2.32
## block:target 0.32 0.20 0.548
## sex 0.74 0.28 0.137
## sex:target 0.32 0.04 0.080
## block:sex 0.32 0.02 0.037
## block:sex:target 0.05 6.64e-05 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 1000.391 ±0.63%
## [2] block + participant : 0.2045083 ±2.11%
## [3] target + block + participant : 208.9854 ±4.55%
## [4] target + block + target:block + participant : 3.962838 ±1.47%
## [5] sex + participant : 0.2595325 ±1.31%
## [6] target + sex + participant : 264.2006 ±1.07%
## [7] block + sex + participant : 0.05294644 ±1.34%
## [8] target + block + sex + participant : 61.77361 ±1.43%
## [9] target + block + target:block + sex + participant : 1.049153 ±1.7%
## [10] target + sex + target:sex + participant : 25.60642 ±1.53%
## [11] target + block + sex + target:sex + participant : 5.955847 ±1.63%
## [12] target + block + target:block + sex + target:sex + participant : 0.1042979 ±2.2%
## [13] block + sex + block:sex + participant : 0.01499254 ±1.42%
## [14] target + block + sex + block:sex + participant : 20.82992 ±6.46%
## [15] target + block + target:block + sex + block:sex + participant : 0.3305103 ±3.13%
## [16] target + block + sex + target:sex + block:sex + participant : 2.004235 ±4.62%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.03290446 ±2.16%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.003774115 ±3.08%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 371.89
## block 0.74 0.19 0.084
## block:target 0.32 3.43e-03 0.007
## sex 0.74 0.24 0.112
## sex:target 0.32 0.02 0.047
## block:sex 0.32 0.01 0.032
## block:sex:target 0.05 2.36e-06 4.25e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 50584.64 ±1.7%
## [2] block + participant : 9.853315 ±0.62%
## [3] target + block + participant : 793933.5 ±0.85%
## [4] target + block + target:block + participant : 419148.8 ±43.04%
## [5] sex + participant : 0.3078975 ±0.66%
## [6] target + sex + participant : 17205.9 ±6.84%
## [7] block + sex + participant : 3.133069 ±1.08%
## [8] target + block + sex + participant : 315522.9 ±12.56%
## [9] target + block + target:block + sex + participant : 76145.02 ±2.14%
## [10] target + sex + target:sex + participant : 3016.236 ±4.84%
## [11] target + block + sex + target:sex + participant : 49929.65 ±2.77%
## [12] target + block + target:block + sex + target:sex + participant : 14808.64 ±2.33%
## [13] block + sex + block:sex + participant : 2.499968 ±1.6%
## [14] target + block + sex + block:sex + participant : 269681 ±3.8%
## [15] target + block + target:block + sex + block:sex + participant : 76622 ±1.59%
## [16] target + block + sex + target:sex + block:sex + participant : 50729.01 ±2.41%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 16401.42 ±3.53%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1327.264 ±2.7%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 4.58e+04
## block 0.74 0.97 10.51
## block:target 0.32 0.28 0.845
## sex 0.74 0.41 0.252
## sex:target 0.32 0.06 0.146
## block:sex 0.32 0.19 0.516
## block:sex:target 0.05 6.16e-04 0.011
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 6476.102 ±0.91%
## [2] block + participant : 39.37768 ±1.03%
## [3] target + block + participant : 424078.7 ±1%
## [4] target + block + target:block + participant : 343068 ±3.64%
## [5] sex + participant : 0.2344488 ±0.88%
## [6] target + sex + participant : 1765.837 ±9.74%
## [7] block + sex + participant : 9.618739 ±3.66%
## [8] target + block + sex + participant : 109645.7 ±2.05%
## [9] target + block + target:block + sex + participant : 82615.23 ±8.1%
## [10] target + sex + target:sex + participant : 151.7267 ±1.46%
## [11] target + block + sex + target:sex + participant : 10639.8 ±3.56%
## [12] target + block + target:block + sex + target:sex + participant : 8623.294 ±4.17%
## [13] block + sex + block:sex + participant : 2.181802 ±1.79%
## [14] target + block + sex + block:sex + participant : 26306.46 ±1.69%
## [15] target + block + target:block + sex + block:sex + participant : 22746.42 ±4.25%
## [16] target + block + sex + target:sex + block:sex + participant : 2624.064 ±2.28%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2352.627 ±4.1%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 109.3815 ±3.58%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 7.09e+03
## block 0.74 0.99 43.94
## block:target 0.32 0.44 1.71
## sex 0.74 0.26 0.124
## sex:target 0.32 0.02 0.052
## block:sex 0.32 0.05 0.119
## block:sex:target 0.05 1.05e-04 0.002
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 43.18236 ±0.93%
## [2] block + participant : 3.415516e+13 ±0.68%
## [3] target + block + participant : 6.764914e+15 ±2.13%
## [4] target + block + target:block + participant : 4.680747e+17 ±1.74%
## [5] sex + participant : 0.1871165 ±2.72%
## [6] target + sex + participant : 8.777375 ±8.85%
## [7] block + sex + participant : 6.563817e+12 ±1.65%
## [8] target + block + sex + participant : 1.270513e+15 ±1.61%
## [9] target + block + target:block + sex + participant : 9.275522e+16 ±2.89%
## [10] target + sex + target:sex + participant : 0.7585954 ±2.07%
## [11] target + block + sex + target:sex + participant : 1.286302e+14 ±2.15%
## [12] target + block + target:block + sex + target:sex + participant : 9.575593e+15 ±2.62%
## [13] block + sex + block:sex + participant : 464956404192 ±3.87%
## [14] target + block + sex + block:sex + participant : 7.457204e+13 ±12.06%
## [15] target + block + target:block + sex + block:sex + participant : 6.207122e+15 ±2.05%
## [16] target + block + sex + target:sex + block:sex + participant : 9.004011e+12 ±3.94%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 6.333224e+14 ±3.34%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.342138e+14 ±9.56%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.08e+03
## block 0.74 1.00 3.88e+15
## block:target 0.32 0.99 150.93
## sex 0.74 0.19 0.083
## sex:target 0.32 0.02 0.039
## block:sex 0.32 0.01 0.026
## block:sex:target 0.05 2.29e-04 0.004
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any sex effects for path length.
Overall, in considering all analyses for device and sex comparisons, we find some differences but these are not consistent. These are likely due to the uneven sample sizes, where we have less mouse users and males in our data. Some of the differences we find involve mouse users overcompensating for the near target, and males having faster completion times than females. However, these differences were small and are likely not meaningful effects.